I have sort of the same problem as you. I spend most of my time in school and studying, so it's very hard to try to watch and read all that I would like too. Right now I'm so far behind I believe I just might never catch all of the great anime/manga out there (there's so much...sometimes it can be a little overwhelming...@.@/*o*....but in a good way, of course ^^).
However, there are a few ways that you can do to get your anime fix and to make at least a little time. (This is what I do anyways):
#1: This forum is a great source for info--just check out the different anime sections for a few minutes whenever you can ^^
#2: When you see a discussion about a series you think would be interesting, check it out online. If you like it, next time you get the chance--pick it up and start with that. (OR--for all the impatient ones out there--or perhaps not so financially fortunate as others [I, myself fall into this category], there are different sites where you can download anime instead of buying)
#3: What should you be watching? Well, there are many great shows out there--it really depends on your interest area--I shouldn't be the one to tell you.
#4: Making time: Just set aside, maybe fifteen minutes to check out different series you might like and look up new releases. It doesn't take all that long if you know beforehand what you want to look for.
I hope this helps somewhat...however vaguely. ^^