Pick a head unit from Pioneer, Alpine, Eclipse, Clarion, etc that has the features you want in your price range. I'd suggest good component speakers for the front and a set of coaxials for the rear, generally the top shelf head unit manufacturers don't make top shelf speakers, MB Quart, Focal and Rainbow are supposed to be the better sounding speakers, Boston Acoustics, Infinity, Polk and Kicker would be good, anything like Kenwood, or Pioneer I'd pass on. If possible you want the component tweeters to be mouonted roughly ear level and firing toward you (like a set of home stereo speakers) rather than firing into the windshield or towards the opposite side of the car. If you have factory component speakers you might not get the best placement possible, but it will look a lot cleaner to use the factory location.
I disagree with the above who claims the amp will make the sound good or bad, while a bargain basement amp may sound bad, an average or better amp should have lower distortion than the speakers. I'd personally put more money into good speakers if you have to choose one or the other. High end speakers will resolve details in the music you'd never know were there if you had a high end amp and average speakers. I'd pick a 2/3/4 channel amp with built in cross over. If you decide to add a subwoofer in the future you can power the rear speakers off the head unit and bridge the rear channels of the amp to power a small subwoofer.
If you choose to install an amp, be aware that the installation becomes several times more difficult, you'll have to pull wire for the speakers, power and signal cables, in some vehicles this is easy, in others it can be a challenge to do without making it look like a hack job.