I have these:

(Click the pic for more info)

They sound great, produce way more bass than I'm comfortable annoying my neighbors with (but the sub has its own volume so you don't have to annoy them), and they're really solidly built. They go for about $80.
Before these speakers I just had a set of $25 no-name 2.1 speakers from WalMart.

One of the cool things about the Z4 is that it accepts an auxiliary input (headphone input) that does NOT mute the main input. So you can connect your ipod to the speakers and still be able to hear your PC through them. I had my Xbox 360 set up on my desk using my PC monitor for a while and had the 360 running through the speakers' aux input. It allowed me to play music from my PC while still hearing the Xbox 360 sound. Really convenient.

You can go with a system like Mod showed.
You can go with a similar system, but upgraded to slightly bigger.
Or you can upgrade quite a bit...

Your computer has the mini-jack output. Shown in this picture, that's what I'm using too because that computer in particular doesn't have an optical output. My new one does and my 2nd HDD arrives today and I already have Win7 downloaded so I should have it up and running by days end. Once my new one is going, I will have Dolby digital surround instead of dolby prologicII.

You may notice my surround speakers sitting on something black. Those are Cerwin Vega towers with a 12" woofer. I actually used those in the dorms and highly recommend them. Everyone...(and I mean everyone) will appreciate them. I use them as speaker stands now.

Freedoms lost are seldom restored.

"A government big enough to give you everything you want, is big enough to take away everything you have" Thomas Jefferson

"Laws that forbid the carrying of arms . . . disarm only those who are neither inclined nor determined to commit crimes . . . Such laws make things worse for the assaulted and better for the assailants; they serve rather to encourage than to prevent homicides, for an unarmed man may be attacked with greater confidence than an armed man." Cesare Beccaria, 1767 (Later quoted by Thomas Jefferson)