The Z-5500s are actually pretty decent sounding speakers. Yes you can do better, but you're going to be spending quite a bit more very quickly (unless you get a very good deal, such as a used reciever). The reason the Logitechs are liked so well by most people is that they've been setup to sound in a way people like (the speakers are overly bright and the sub puts out a lot of bass, although its not tight, high quality bass). Audiophiles like neutrality and clean crisp sound, which isn't what the Logitechs provide, which is why you'll find people who absolutely hate them. Its really preference as much as anything there.
There really isn't much lower priced than them that will do what you want. If you just play it single player and online multiplayer, then you could pick up a reciever and some nice headphones like the Sennheiser HD-280s or HD-555s. The sound quality will beat most speaker systems and while you won't get true surround sound, you aren't missing too much (sound quality over quantity).