It really depends on what kind of game it is. If your game is any type of the following, you'll need a fast computer to drive the server:
-games that are very server based instead of client based: BF1942, BF Vietnam
-games with bots: UT with bots, CS with bots, Quake with bots
-games with a lot of stuff going on: Neverwinter Nights
-games with lots of players connected: any game
-games with advanced physics: Half-Life 2 apparently
As for playing and hosting at the same time, yes you can do that, but only if you give the server priority over the client. If you give the server priority, the clients will not lag, but you will have low frame rates. If you don't give the server priority, your frame rates will be ok, but everybody on your server will have 400+ ping.