what would be a good speaker system to buy

A good set from a company like Altec Lansing, Audioengine or M-Audio, depending on your budget.

Logitech is really not that great for speakers.

Poor, misguided individual. Coming from an upcoming audiophile: Why is loudness so important? The louder the music is, the less time you get to spend enjoying it due to deafness. The louder your music is, the more police you get to know. The louder your bass is, the more your house rattles, the more unpleasant the sound is ;) I've been there, done that.

What does "more bass" mean? Are you referring to louder bass, lower frequencies or better bass response?

If you want louder bass, just get any 12 inch subwoofer with the highest wattage possible for your money. 12 inch drivers are generally louder, but less responsive than 8 inch drivers. The 8 inch drivers would also generally be able to generate lower bass frequencies. Now, having said that:

1. You can't just get 2 drivers and the loudness will magically double. It doesn't work like that. Standing 2 metre away from 2 speakers won't be the same loudness as standing 1 metre away from 1 speaker. That's dependant upon the amount of power your amp is pushing to the speakers.
2. If you have money (which you don't) you CAN get better response and lower frequencies from 12, 15, 18 and 21 inch subwoofers by making isobaric enclosures. In an isobaric setup, you have 2 speakers wired out of phase in a single box, so that as one pushes out the other pulls in and they do this thousands of times per second.

My advice: Save your ears, and your money until you can buy something better. I'm not sure about this whole 5.1 thing, either. I may be young in terms of the life of music, but I thoroughly recommend a separate amplifier for each set of identical speakers, a range of speakers from 8 inch to 21 inch and some decent midrange/tweeters, when you can afford such a setup ;)

I've rambled on enough, but I hope I managed to help...

Speakers for your HDTV

CineMate® Series II home theater speaker system

Designed to enhance the audio from your TV and existing video sources Connects directly to your TV, no receiver required Available with Gemstone speakers and universal remote or Articulated Array® speakers and simplified, four-button remote. $599.95