I would suggest you are careful in selecting a router. All of them seem to offer similar functionality, but it's my belief that some are more limited than others.
For instance, I bought an SMC7004VBR because the price was excellent ($39.99 CDN). It seems that this router inparticular has some issues with the number of option connections it can handle at once. For instance, when I use gamespy, or ingame browsers to list servers, I can list about 350 servers before the router quits handling incoming packets and won't let me make any new outgoing connections. This subsides in about 3 minutes, and I'm able to have normal use of my connection again, unfortunately I can't join any of the servers I've listed, or otherwise make new connections, until this time is up.
Feature wise, this router is quite nice, offering alot of NAT options, etc. It doesn't allow you to easily map entire port ranges without a trigger port, however, something that would be quite handy.
So, all in all, a router shouldn't affect your ability to JOIN online games. It will definately make hosting games difficult as you will need to manually open ports. Ask someone you trust (preferably a gamer) how their router works for gaming. I have friends with linksys routers that work fine for listing servers, etc.
Oh, and one last word of advice... You pings when listing servers will be higher than when you actually join the game. Right now mine are about 30ms higher in the server list. If you turn on any intrusion detection or Stateful packet inspection stuff in the router you will make this value higher, although how it affects actual gameply, I can't say.