One thing always comes to my mind: if I am a good photographer, I can't take my own photographs! Only other people can take my photograph.
Can anybody suggest the best way to take self photographs, and which camera is best for this?
Tripod and a timer or remote trigger. Setup the shot, set the focus point where you'll be standing, take your position and click off a bunch. You can also rig up a more complex setup where you can remote view the shot on a laptop or tablet (or even a smartphone) before taking the photo so that you can make adjustments remotely, but that's a bit more technically complicated to do.
It deep-ends what you want to achieve.
"Good quality" "normal" photos can easily be obtained with a timer - having a display that allows you to check framing is a bonus. Using a remote shutter release helps heaps. There are after-market wireless releases available for most brands. This is often a "key fob" sized device that you can hide in your hand so it is not seen in the photo.
Using a short shutter delay is useful for self photos. You then don't have to hide your shutter pressing actions or "face". 2 seconds is usually enough. If your camera does not support this some after market wireless releases with built in timers.
A "fully articulated" display such as on the Sony A99 shown here allows you to compose the image from "in front of the lens".
"FOR THE RECORD" PHOTOS
If you are interested in eg trip photography proof-of-life Kilroy-was-here just-for-fun type images then you can get "very reasonable results with a DSLR held at arms length. This takes some practice but if you add a local or 2 or 3 it can be great fun. I am right handed but a std DSLR usually works better reversed at arms length when held in the left hand.
That this is what is being done is often obvious once you are aware it is being done, but many people look at the photos without realising.
It is extremely useful to have an articulating LCD that allows you to see the image that you are about to capture BUT you should not look at it as the photo is taken. Below, in image at left subject is looking at LCD above camera and eyes are obviously "not right". Subjects need to look at lens front as photo is taken. Two images at right show that "reasonable results" can be obtained. Aficionados will decry on-camera flash :-).
With multiple people in the image the photographer needs to be at far left (image right) OR the person at image right must be behind your arm. Not a problem but worth noting - eg see top left image below (lady on image right there and in lower left image is my long suffering wife). (Nobody wants to know, but: L2RT2B Malacca, Urumqi, Ningbo, Donguan, Polyfest, Xian, Malacca, Urumqi, Yogyakarta, Urumqi).
For extra points or in tight or specialist situations - such as hanging off the outside of a speeding train, you can use a short tripod (say 2 feet / 600 mm) with the camera pointing almost "down the legs" and then hold this at arms length and use a timer. eg set focus point, swing camera in, press shutter button, swing out/pose/hold tight to train - click, repeat as required. I find that a 2 second timer is OK for this - holding camera on tripod at arms length for 10 seconds is somewhat demanding.
Two second timer. Small tripod with legs fully compressed, held at arms length. Safety strap advised :-). [Malaysia]. Exposure & focus & white balance - terrible. Memories of occasion - priceless.
FWIW: Imgur stores these images at higher resolution than they are displayed. Windows/GargoyleMail right-click on image and select "Open image in new tab" opens a larger image than is displayed directly. Other OS / Client combinations will presumably do similarly. In this case full accessible image is 2164 x 1410 (compared to about in this case 790 x 515 on my just over HD LCD).
NB - if participating in potentially dangerous acts to acquire your holiday photos, be sure to not lead others astray. The camera at above left is looking in the direction of travel. This is "safe enough" if you do not fall off AND if you avoid trackside obstacles. The young woman who saw me "playing" and came and joined in was oblivious to such dangers and I had to forcefully emphasise how easy it would be to die.
There is one thing called shutter release, many great photographer in the history use it to shot their own portrait.
Or you can just shot it with your mobile phones. Don't you think I‘ts great that some other takes a photo of you？That would make you know how are you in others eyes.
A camera with flip screen is great for casual selfies.
If your camera does not have a flip screen but does have live view, rather than the obvious "point to the mirror" you can always point the camera directly at you and peek the LCD screen reflected in the mirror.
Another interesting option (if your camera supports it) is using the camera in tethered mode and check the framing and shoot from a computer or a tablet.
But I think the best way is to teach a friend how to make nice portraits and let them take your picture.
The best way to take self photographs is a) shooting a video and no photo (with timer) b) using a display that can be swiveled so you can monitor what you are shooting b) selecting the best still from the video.
The quality is limited to full HD (or 4K with some advanced cams or smartphones like the Note 3 and others). But this might be enough for your needs. The chances to get a good shot are much higher when you can relax while the video rolls. Try different angles and poses.
Whether you're using your camera or smartphone, you don't want to have it in the frame. Instead, hold it away from you at shoulder level and twist your body toward it, pushing your opposite shoulder toward the camera. Then crop the arm that's holding the camera out of the pic.
Advice for the rest of your life
Hire a professional. Be you and let a pro concentrate on capturing your personality and how you project yourself. I consider myself a pretty good portrait photographer, yet, my favourite photos of "me" were shot by colleagues. Mine now look contrived and disappointing.
I think the advice also applies to hiring a lawyer. It's not a do-it-yourself project. As the saying goes, Whoever acts as their own lawyer, has a fool for a client.
Maintenance is fine for me; but, I still visit my dentist.
You see where I'm going with this. Treat yourself!
Use a mirror, so you can have a self-portrait as a photographer and show your favorite camera.
Painters have used this trick for ages.