Decking out your car with new speakers is no easy gig, especially since before you get to the guts you have to pick which setup and gear you want. There are a few things to take into account before deciding on any car audio - not the least of which is the size of the speakers you want. For what it's worth I suggest 6x9 car speakers, and you'll soon see why. First off, though, figure out where you're going to mount your new hardware. You don't see them often in the front or doors anymore, especially with the size we're talking. Most of the time car speakers are mounted in the trunk, due to space concerns. Still, if you're on the creative side, maybe putting them in a customized console in the back seat area, or even replacing the back seat are potential options. It all depends on whether you want to show off the speakers themselves and the audio, or just the pure sound output power. There are many brands to consider, but I'd recommend Alpine, Pioneer, Panasonic, or Sony - go with a mainstream brand since they know what their doing, you'll be able to find the best deals on the gear, especially on the internet, and you'll get the best support and the easiest installations.
Second thing is whether you want a dedicated system that's only composed of new stuff, or do you want to augment your existing audio system with some choice components. Some high end gear can really change the sound in the exterior and interior, but if you go with all new stuff, you might end up with an overall better system. Of course, you'll definitely end up spending more, especially if you're going for high end audio components, which don't come cheap. Also, the higher end you go with 6x9s, the more supplemental gear like amplification you may need - so it's a good idea to know what level of sound and how much you're willing to spend before you go shopping. Your car most likely won't have speakers this size already installed, so you'll likely need extra amplification to handle all the additional sound throughput you'll want to hear. You could try wiring the speakers directly to your stereo's outputs, this is almost certain to leave your 6x9 car speakers underpowered - and when you're both shelling out and showing off such large speakers, there's no reason not to have full, big powered sound to go with it.
6x9 car speakers are in demand because for their size they're super powerful. The standard woofer cones that come factory installed on most cars don't stand a chance when stacked up to a beefy set of 6x9s. And as a bonus, they often come with integrated tweeters built in to the unit, for extra punch in the higher range. Coupled with the boost to the mids you get from the 6x9s, we're talking a lot of sound - with smaller speakers you might actually end up taking up more space due to needing more components and more install time. Given the limited amount space in your car available for audio modifications, versatility and economy are the watchwords here - you could get giant speakers, but you'd have no way to cart them around given most cars' setup.
So as you can see, car audio isn't really a cut and dried, one size fits all problem - there are plenty of decisions to make before you arrive at the showroom. Specifically, where are you going to mount the speakers? You have to decide whether it'll be a regular panel mount that inserts into the door panel, or wall panel of your car, or the floor of the trunk, or even the back of the back seat. The alternative is to box the speakers and create an optimal surround somewhere else in the vehicle - most likely the center. This second choice is definitely more work, but will leave you with the best sound quality once the installation process is done. That brings up a good point about audio output, however. 6x9 car speakers excel at mid-range sound output, and will help you out on the low end frequency sound too - you may even get by with a smaller subwoofer than you'd originally planned.