This is nearly exactly what I am doing. First off I would suggest scraping your laptop's built-in audio right from the get-go. Go get yourself a good external USB soundcard like the Creative Sound Blaster Extigy:
http://www.creative.com/products/product.asp?category=244&subcategory=249&product=585
Once you get this, you have many better options for audio in/out, midi, recording, playback etc... Such as 5.1 channel sound, line-level inputs/outputs. Though this Extigy I can't see if it has line-out. If you plan on using an amp you definitely want to have line level outputs for the cleanest signal.
For your amp you'll need to leave the PC world and get in the audio world. Check out amps from the likes of AudioSource
http://www.audiosource.net/amplifiers.html : Behringer
http://www.behringer.com/02_products/group_index.cfm?mid=2&ID=200&lang=ENG : Mackie
http://www.mackie.com/products/amplifiers/index.html : and anybody else who sells "power amps".
If you are on a budget, you can get by with using your headphone jack into an amp into your speakers. But don't expect high quality.
On the other hand, if you want to pump a DVD movie out to your 5.1 speakers, you'll want the USB sound card with a 5.1 decoder.
You have a lot of options, but the AMP may cost you some booku bucks. Because you'll soon find out that audio amps are a lot more expensive then car amps. But I would highly suggest not trying to fuddle with using a car amp, not wise. And car amps are nowhere near the quality of standard audio amps. Just not as clean, they don't have to be. And the power supplies are a real issue.
Lastly, don't buy an amp with such high watts it blows out your speakers! You want to match them up fairly close.
To be honest, I've yet to find a decent AMP I can afford to drive the two tower speakers I have right now! I'm in the same boat you are. And they use the two-wire speaker cable as well. Which you'll want to be sure the amp outputs to this, or often called banana plugs too.
If you end up buying an amp, tell me which one you got and if it works good! lol