The noise you refer to is most likely the dreaded "ground loop". The only real way to not get it is to not use the cig lighter (assuming you get the noise in the first place, you may not) and run a dedicated power source and an isolated ground.
You pretty much got the only two real ways to get sound out of the pc. You could use an fm modulator, but I wouldn't recommend it.
If you are keeping your HU, just use the aux in. You can't easily run a seperate amp and a hu together through the same speakers. You can, but it's a major pita.
If you're looking for a relatively quick and easy solution, the aux in is the way to go.....
Either way, sound quality will be ok, but not exceptional. If you're just a casual listener looking for tunes while you drive, I don't think it will matter if you use the onboard sound or an external card. Plus, you're going to the HU anyways..........
An amp requires power and a remote turn on signal at the least.
Sorry, not a whole lot of help, but it's all I've got for ya!
Good luck with your build.