That depends on what kind of entertainment you need in the car. Nowadays it can range from a simple FM Radio to car theater integrated fully functioned computer system with GPS tracking and bla bla bla.
Because you just step up from factory system, I assumed you just need a simple stereo system to enjoy music with better quality than the stock system.
You can star by picking a good quality CD receiver head unit. Recently good ones come cheap, with about $100-$150 you can get decent CD player with Radio, sometimes with aux-in, USB, and iPod compatibility. There are some good entry level ones from Pioneer, Alpine, Sony (I suggest you choose from big brands, the build quality is usually better and has better after sales support)
Next is to find a good quality speakers. Now it's depends on how loud you want the system to go, how much you want to sacrifice the integrity and space of your interior, and oh, yes, your budget. If you want a simple system, just buy some good coaxials and install them in stock factory panels, it can be 5", 6", or 6"x9" depending on your car. If you have the space, I suggest you install a seperate component speaker (the one with one tweeter and one woofer for each channel). Power them from head unit if you have limited budget, if you have extra, buy a 4-channel or 5-channel amp.
For a limited budget, here is my suggestion :
Install a decent quality 5" or 6" component speakers at front, put the woofers on the factory's hole and the tweeters on the dash corner near the A-pillar. Next buy a 4-channel power amp (a decent one with 50W/channel will cost you about $200), take 2-channel to drive the front speakers, and the rest bridged to drive a subwoofer. A 10-inch is enough, my recomendation would be JL Audio's W0/W1, or Kicker's Comp. Build a small sealed box for the sub.
Rear speakers? You can power them from the head unit, you don't even have to change the stock speakers if they're not broken, in driver's seat you won't hear much of them anyway.
E-mail me if you have another question
Good luck