Here is my workflow, but everyone is a little different.
I shoot and mark the rolls, if necessary. For example, if I know a roll needs to be pushed in development I will mark that on the roll.
If it is color I send it to a lab and to process and scan. I have done a lot of color and I know I don't really want to deal with the hassle and expense of color chemistry.
If it is B&W film, I process it at home in my JOBO processor. I personally use XTOL diluted 1:1. I find this to be a great all around developer.
I dry my film in a film dryer I made. It is basically just a box with a filtered computer fan on the top and bottom pushing air through. I try to keep the room I process in relatively humid to help keep dust under control. This is not necessary, I used to hang my negatives to dry in the shower, but I had to deal with dust more when I did that.
Then scan my B&W on an Epson V700. It is a flatbed scanner that does a pretty good job for it's price. There is a lot that you can do to make this a REALLY great scanner. 3rd party negative holders, ANR glass, different software, etc. But a lot of that is more expensive than I am willing to deal with.
I scan at 1200 DPI, 16-bit greyscale. I can go higher, but I don't on my initial scans. I can always come back and do it again.
For color I usually just have my friend at a local lab scan it for me, since he is already developing it and he does it for me for free. But even if it wasn't free I would still probably not scan my own color because the software for the Epson (and literally ever other scanner I have ever used) kind of sucks. It can be difficult to get the colors you want. So I let someone else handle that for now.
Now I have digital files I can bring into Lightroom. When I bring them in I make sure I tag the files with the camera, lens, film, and process variations (if there are any, i.e. pushed +1, cross-processed, etc)
For the negatives, I buy sleeves from Climax Photo Supplies and label the sleeve with the year, camera, lens, and process variations.
For the editing, first I cull, then crop, then adjust color and contrast. But that is generally about it for color film.
B&W is a little more involved because I have to remove dust from the scan.
You're probably asking "Why do you not have to remove dust from color film?" Basically, film works by little pieces of light-sensitive material being suspended in emulsion on the film. For color film, part of the chemical process of development basically stains the emulsion, then the light sensitive silver gets bleached out of the emulsion, leaving just the stain. That is what we see on the film as the negative.
For B&W it is a little different. A lot of silver gets left on the negative after processing.
Why does this matter? Most modern scanners have a for of something called digital ICE. This uses an IR scanner in addition to the regular optical scanner to determine where little pieces of dust are on the negative and compensate for that in the software. It usually does a pretty good job of this. But because there are so many little pieces of silver left on B&W negatives, you end up with the scanner trying to "clean" most of the image up. It just doesn't work. So for B&W film the scans need to be cleaned manually.
There are a lot of ways to simplify this process or adjust it to fit your needs but this is a good balance of convenience and loving the process for me.
My recommendation would be start off by sending your film out to a good lab. My personal recommendation is Boutique Film Lab. I know the guy that runs it and he does a great job and cares about putting out quality work.