I would like to purchase my first DSLR camera with similar features and experience to my AE-1 Canon film camera. In particular, I would like a depth of field indicator that shows the depth of field in feet. I did not like the gauge I have seen in other digital cameras whose indicator shows the range from a picture of a flower to a picture of a mountain. What cameras do you suggest that include these features?
DoF scales on lenses is pretty much of thing of the past (see: Why did manufacturers stop including DOF scales on lenses?), mostly due to the fact that zoom lenses and autofocus are ubiquitous and commonly used. A DoF scale changes with focal length, and autofocus has made the focus "throw" of a lens much much smaller than in manual focus days, so using a DoF scale with any precision with manual focus is problematic. And, well, you've got autofocus, which tends to be pretty accurate. And DoF preview buttons can help you estimate what the DoF is, as well as possibly a DoF scale in the viewfinder.
These days, manual focus aids include liveview features, like focus peaking and magnification. Not DoF scale focusing and split-circle focus screens.
I don't think you're going to find another dSLR that has exactly what you're envisioning. What you need to focus on is what is your budget for this dSLR, what kind of performance do you want? And what format of sensor will deliver for you?
If you want a dSLR or other interchangeable-lens body that's similar in feel-in-the-hands to your AE-1, chances are good you'll have to go with a mirrorless body. dSLRs are much larger than their manual film counterparts, because of features like autofocus and autoexposure. For a similar-sized body, something like a Fujifilm XT model might work, or the Olympus E-M series. And chances are good you could use your lenses with an adapter on these mounts.
But if you want something that feels and operates, menu-like, like your old Canon, than a Canon dSLR might be better, but you'd have to swap to EOS-mount lenses. OTOH, unlike Olympus or Fujifilm digital cameras, you also have the choice of a full-frame sensor, which is a sensor that's the same size as a frame of 35mm film, so things like DoF and FoV vs. focal length, and the view in the viewfinder will be more similar to what you're used to with a film SLR.
I would like to purchase my first DSLR camera with similar features and experience to my AE1 Canon film camera.
It's going to be a very apples and oranges kind of comparison. When Canon introduced the AE-1 Program in 1976, it was very advanced and made it a lot easier to take correctly exposed photos. But today's cameras have more and different features. Digital photography can be just as much fun as it was, but you should be prepared for some differences.
In particular, I would like a depth of field indicator that shows the depth of field in feet.
The DoF indicator was a feature found on most, if not all, SLR lenses back then. It was really just a set of symmetrical marks, one on each side of the focus distance indicator line, for each of several aperture settings. You can still find some of those marks on some Canon and third party lenses today, but there are fewer of them if they're there at all. For example, the Canon EF 50mm f/1.4 has a set of marks for f/22, but that's it. Zoom lenses tend not to have them at all, perhaps in part because the push-to-zoom design that was so common back then is hardly seen at all now. Those old lenses had a set of curved lines that showed depth of field at different focal lengths as the zoom/focus ring moved, but newer designs don't allow for that.
The good news is that you really don't need the depth of field marks because every digital camera features a big display that lets you see the photo you just took, and you can zoom the image to check focus at any point. You didn't have that kind of instant feedback in the old days; you had to estimate the depth of field and maybe try to check it by stopping down with the DoF preview button, but you never really knew if you got it right until you developed the film, which could be days or weeks from when you took the photo.
I did not like the gauge I have seen in other digital cameras whose indicator shows the range from a picture of a flower to a picture of a mountain.
I think you're probably thinking of the icons for some "scene" modes. Many cameras have a number of automatic modes where the camera will try to optimize everything according to the kind of photo you're taking: landscape, portrait, close-up, sports, etc. Most cameras that aren't aimed solely at professional photographers have these modes, but you can ignore them and set the camera to the manual (M), aperture priority (Av), shutter priority (Tv), or program (P) modes that you remember from your AE-1.
What cameras do you suggest that include these features?
Any DSLR will include the exposure modes mentioned above. Your choices will really come down to your budget and a comparison between features that didn't exist 40 years ago: number of autofocus points, autofocus speed, sensor size, burst rate, video capabilities, and more. If you don't care about any of that and really just want a digital version of your AE-1, look toward the low end of any reputable manufacturer's lineup. For example, the Canon Rebel T5 is currently available refurbished for as little as $320.
It really all depends upon exactly which part of the AE-1 experience you most wish to replicate. How the controls with which you set the camera look and feel? What you see when you look through the viewfinder? Size and weight? Image quality? A sensor size that preserves what you have learned regarding focal length, field of view, aperture and depth of field?
There are a few cameras that have (1) The "feel" of those old SLRs with knobs and buttons to control things such as shutter speed, aperture (which is rarely set via a ring on the lens any more), and ISO that look and feel like the controls you are used to using and (2) Have bright optical viewfinders and (3) Use a sensor the same size as the 36x24mm film frame of your AE-1. Most of them are a lot pricier than an entry level DSLR, though. They're even significantly more expensive than the cheapest full frame DSLRs. They're also larger and heavier than your AE-1. The Nikon Df is one such camera (leather case and strap optional).
There are cameras that are as small and light as your AE-1, but most of them require digging through menus using the rear LCD screen to change many of the settings with direct controls on your AE-1. Many mirrorless cameras, particularly a group from several manufacturers known as "micro four-thirds" that all use the same lens mount would be in this category. The main drawbacks of these cameras compared to your AE-1 are: (1) The lack of a through-the-lens optical viewer if they have an eye-level viewfinder at all and (2) Smaller sensors that impact image quality, especially in low light situations. The smaller sensors also mean everything you ever learned about the relationship between focal lengths, angles-of-view, and depth of field will need to be relearned. The Olympus OM-D E-M5 II is such a camera.
APS-C DSLRs will give you a sensor (and image quality) better than the micro four-thirds cameras. They will also give you an optical viewfinder, though it will be smaller and probably not as bright as the one on your AE-1. But entry level APS-C cameras start at about 1/3 the price of the cheapest full frame models and are a good way to get started with digital photography as they allow more room in the budget for quality lenses. They'll allow you to get good pictures on a budget like you could get with the AE-1, but they won't "feel" as much like shooting with the AE-1 did. The Pentax K-S2 is available in various color schemes, here are just three of many.
To get a camera with any kind of viewfinder comparable to the size and brightness you enjoyed with the AE-1 you'll need a full frame DSLR. Those tend to be larger and pricier than the entry level DSLRs with smaller APS-C sensors. But they're the closest thing to your AE-1 (without breaking the bank on something like the Nikon Df) in terms of image quality and what you see through the viewfinder. They also preserve your knowledge of the relationship between focal length, field of view, and depth of field. The Canon EOS 6D is one of the most affordable full frame cameras on the market.
Which brings us to the subject of depth of field and scales on lenses for focusing and figuring depth of field:
In the digital age Depth of Field (DoF) is a much harder nut to crack from a camera design perspective than it was in the days when a photo from a camera such as your AE-1 was rarely printed larger than 8x10, and most images were viewed at 3.5x5 or 4x6. Now people routinely view images on their 20-23-27 inch computer monitors not only scaled so that the entire image is visible, but also zoomed in to 100% so that each pixel in the image equates to one pixel on the monitor. That means that a 24MP image viewed on a 23" HD (1920x1080) monitor at 100% is like viewing a small piece of a 60x40 inch print! It also means that the circle of confusion used to calculate DoF varies too much between one extreme and the other to make a single DoF scale like those on old lenses accurate.
This is further compounded by the possibility of using some lenses on cameras with different sensor sizes. As the sensor size changes, so does the magnification ratio needed to view an image at a standard size. This also changes the circle of confusion needed to calculate DoF. If a lens that can be used for both full frame and APS-C cameras is accurately marked with regard to DoF for an 8x10 print when used on a FF camera, the same DoF scale will be incorrect for an 8x10 print produced with that lens mounted on an APS-C camera with the smaller sensor.
With such a wide range of variables (sensor size, intended viewing size, intended viewing distance) the range of circles of confusion needed to calculate depth of field for a particular focal length, aperture, and subject distance is just too large to put meaningful DoF scales on lenses.
Face it, even the best DoF scales on lenses in the film era weren't all that good for anything beyond an 8x10 print. Even then the photo books we read taught us to divide the DoF by two if we planned to make a large print. But those scales were better than nothing when we couldn't see the effect of changes in aperture, point of focus, focal length/shooting distance, etc. until later when the film was developed and the opportunity to adjust based on those prints had long since passed. Now we're afforded the opportunity to look at the results immediately and reshoot the scene if we wish (although the rear LCDs on cameras do tend to lie like politicians unless we zoom in to check focus). Using Live View we can even often preview the scene, including the DoF (with the right camera and settings selected) while zoomed in at 10x magnification. This is akin to viewing the scene on a ground glass screen with a view camera before inserting the sheet film cartridge!
Similar experience will be a problem. AE1 is a fairly small camera for todays DSLR standards. If you want something that has similar size, you will have to get a camera with smaller sensor and this is again changing the experience, because the lenses do not behave the same way as on 24x36mm frame.
With regards to the DOF scale, this is a feature of the lens. Your old lenses will not work easily with a new Canon camera, but many modern lenses have the scale, so just choose a lens with the scale when you buy the new camera.
I'd stop worrying too much about the technical details, go to a shop or find friends with modern cameras and just try them out. There are excellent cameras at a variety of price and feature points, which can all take good pictures. Don't go for a simple 'point and shoot' only type of camera if you want to explore more. And don't go for one that has every possible setting and option if you just want a simple camera. In practice, even the most capable modern DSLR or similar cameras will still have a lot of automation that you can use, so you can start using it straight away as a simple point and shoot and explore later as and when you feel like it.
What matters most, beyond almost anything else technical, is what feels right in your hands. If the camera FEELS RIGHT TO YOU, you are far more likely to enjoy using it and take more and better pictures.