If a router says it's wifi or 802.11b or 802.11g, it's wireless. There's also an "A" and "N" standard. N's just coming out, and A is hardly used anymore.
If you just plan to use the internet, "B" is fine. "G" is a bit faster and basically standard with most laptops now. "N" is the fastest, but also most expensive.
As for what router to get, I'd look for a lower end Linksys. You can get them for around $40 and they are pretty nice. Perhaps some of the top rated ones.