I like to run in regular athletic shorts. When I run long, I may go with a running-specific short. I find that they are a bit 'faggotty' for me.
I like to run in my 'tighty whiteys' for support, if you know what I'm saying.
I wear boxers just about all of the rest of the time.
Again, as you run more, you will find what is comfortable for you.
The great thing about running is its simplicity. Everyone owns shorts and t-shirts. The only equipment that you should not skimp on it shoes. Do not run in anything but running shoes. Not cross-trainers, basketball shoes, or any others... running shoes. Don't buy them at a mall store. Find a running specific store that will be able to 'fit' your shoes for you. They will be able to look at your gait and your wear pattern on your shoes to best fit the style of running shoe that will work best.