If It were me, I'd just invest in better speakers for the car, add a sub, maybe try & get a better head unit (one that can support 5.1) along with one of those center channel speakers that mount on or in dash, etc...
would be cheaper with what your thinking, but it would suck, as you'd have to figure out where to mount the speakers etc etc, & would be a real pain in the arse.
I'd go for the 2nd idea, add a sub & amp, & if you can, replace the factory speakers (if they are factory speakers in car) to compliment the sub & amp, as well as the head unit.
later this week I should be picking up my newer car, a 1999 Grand Am SE coupe, with factory sound system (CD & 5 band equalizer), but plan on adding an amp/sub if I can, looking at a couple of Blaupunkt subs & one Infinity sub (all 3 are the lower profile types that save on space & provide good bass, but not enough to rattle the neighbors windows)
also plan on by end of year upgrading the head unit & see if I can't get one that can run DVD's & if possible has a LCD touch screen, but thats IF I have the money for it.
eventually I want to get a nice sounding system, possibly 5.1 if I can. as I've grown accustomed to my 5.1 home theater & sound card on my game rig as my sound system.