First off, what is your total budget?
There have been some good suggestions thus far, just note though that if you go with a stereo receiver or one of the mini amps from Emotiva/Sherbourn, you are going to need a DAC. Your line out on your computer is noisy and you will need something (preferably USB based) to clean that up. Something like a Behringer UCA202 is a great inexpensive choice. If you go with something that has digital inputs, you can disregard a DAC.
The way I see it, if you go with powered speakers, you are going to need a pre-amp of sorts. It is easy to spend a lot of money on this, and that new Emotiva mini pre-amp is nice, but you can also get by with something like a USB mixer. The Lexicon Alpha is a good choice and only about $60 IIRC, the reason I mention this is you will want some sort of accessible volume control, and this also serves as a DAC. Most powered speakers have volume control on the back, and adjusting levels in Windows is not preferred do to possible bit-loss with digital volume control. Ideally you want Windows at 100% and then some sort of volume control to adjust levels. I used to own a pair of powered Mackies and used a Lexicon Alpha for this purpose. It also afforded me balanced connections to the speakers, but that is more of a luxury than a requirement.
I assume this will be a nearfield setup, in which case I would recommend going with a t-amp. They are inexpensive, compact, and offer great sound quality. Because you are sitting at most 1 meter away, it doesn't take much power to make your speakers loud. Assume a speaker has 87dB sensitivity, well it only takes 1 watt to hit that SPL, 2 watts is 90dB, 4 watts is 93dB. At 1 meter away, this is very loud and probably bordering on uncomfortable. A 25x2 t-amp is going to be able to put out a solid 12-15 watts per channel before the THD gets too high, and this is plenty of power. I use a Topping USB t-amp, so my DAC and amp are combined in one package, and it has plenty of power for me. You can get the Indeed TA2021, which is a very good quality t-amp from Ebay for $50. You would need to spend $150-$200 on a stereo receiver at least. Now going with a stereo receiver, or better yet a HT receiver, affords you bass management, room correction, multiple input options, and a DAC, but you have to weigh the cost/space variables. Sound wise they are all going be pretty much identical, so buy what is most convenient based on your needs.
If you do decide on passive, there are dozens of good options. This is where the budget comes in, and also any size requirements/placement limitations. You may need to look at a sealed speaker or front ported speaker if you don't have room behind. Hope I have helped with some of the big picture decisions, once you narrow down your needs, I can offer some specific suggestions.
5.1: Samsung PN60F5300 | Sony BDP-S1700 | Denon AVR-1713 | EMP E55Ti | EMP E56Ci | EMP E5Bi | Outlaw Ultra-X12
2.0: Oppo DV-980H | Apple Airport Express | Topping D30 | Parasound HCA-1500a | Chane A1.4