Let me start by saying that I'm a big fan of all the guitars you mentioned.
So, judging from the genres you listed, I would suggest a Les Paul. Strats and tele's are awesome as well, but not so much for punk or grunge. They have a very clean sound (because of their single-coil pickups, but i won't get into that here) and would be GREAT for blues. Les Pauls have a sound i guess i would describe as a little bit dirty or fat. This tone is excellent for punk and grunge. And it doesn't really matter whether you're playing Rhythm or Lead, you can just adjust the pickups in order to get the correct sound. You can do this on any electric guitar.
Since you're a college student, I doubt you want to drop $2000 on a Gibson. I just bought an Epiphone Les Paul Custom for $700 and i LOVE it. Most epiphones are just made on an assembly line and shipped to the store. However, the customs are inspected and adjusted by a master craftsman after they are built. So they definitely have great quality for the price.
If $700 is too high for you, then I'd suggest a lower end epiphone, like the Ultra or Standard LP's. However, it is VERY hard to find a solid guitar for under $500 in my ever so humble opinion.
EDIT: Remember to give careful consideration when choosing the amp as well, because the amp is equally if not more important than the guitar. A great guitar will sound awful through a cheap amp, but a crappy guitar will sound pretty darn good through a decent amp.
been playing for 6 years or so