Need a router. Don't know much about them

I'm looking to buy a router for my apartment. It's about 1000 sq ft so there's not too much space to cover, but it's possible I'll be in a house within a year or two and then I might need some more range.

I'd rather not spend more than $50 or $60 ish, but I'd go up to 100 for a really good one that I'll get much better performance out of.

I don't want to do anything too fancy with it. My internet connection is AT&T uverse at 12 mbps. There are 2 of us in the apartmnet but I'd like a router that can handle up to 4 or 5 people. I browse the internet and do normal things like facebook alot. I also get alot of streaming music and video like Hulu, youtube, and grooveshark, and I'd like to get good performance out of them. I also do a lot of video chatting so I'd like decent performance in that area. I think an N router would be best but it needs to be able to support g wireless cards also. I don't need any super strong security or anything. As long as I can set a good password I think it's fine.

What benefits do you get from getting gigabit ethernet over the slower one? Is that just for wired connections? If I only had one computer on a wired connection to the router, would it be worth it to get one with a gigabit connection?

If there's any other information I can provide, let me know.

Thanks for the help.