You can replace the stereo with one you buy from Crutchfield if you want. If you go to Crutchfield's website, they will tell you what will fit based on the description of your car. There are other places where you can buy the stuff for less, but Crutchfield has excellent service and knowledge - which is reflected in their prices.
You will need a dash kit and a wiring harness will make installation easier but not required. A dash kit is a basically going to be a plastic frame that goes around the stereo to fill in space because aftermarket radios have standard sizes but stock or factory units are often not standardized. Aftermarket radios have bare leads coming out of them and have different colors than the wires in your car. The wiring harness will connect to the bare leads and then mate directly to the connector for the stock radio. If you don't use one, you'd cut the connector for the stock stereo and splice the wires.
For sat radio you will need an external tuner module. Some modules have a display with their own controls and some utilize the display on an aftermarket radio and the radio's controls. For best sound quality, you want one that connects with a wired connection such as some type of line or auxiliary input. You do not want a FM modulator or transmitter type. The FM type plays through the FM radio and in some urban areas can become completely unusable and may be prone to interference.
Speakers can be replaced if you desire. The factory speakers are often ok quality, not bad, not great. For best sound, it's best to use a component set up front rather than coaxial, 2-way, 3-way types. Components are a little bit more work and usually cost more but I think they're worth it. The back just get a good 2-way or 3-way, or consider removing completely if you get a subwoofer.
Do you want an amplifier for the speakers? Radios have internal amplifiers that usually put out about 18-22W RMS per channel but many people prefer to go with external amps that put out upwards of 30W RMS per channel. More power means better clarity at higher volumes. There is more labor to install an amp due to all the required wiring.
Best Buy, Circuit City, and the like are ok, but I prefer not going to them. They don't have much selection and will not order anything for you that they do not normally stock. See if you can find a reputable shop in your area where you can buy the stuff and install it if you don't want to do the install yourself. They are in a better position to do special order stuff for you.
Some brands I like for radios:
Pioneer
Clarion
Alpine
The above companies make amps and speakers too.
For speakers:
Arc Audio
Diamond Audio
Focal
CDT Audio
These companies make mostly speakers and amps. They are less marketed but their lower line products are just as good as competing products from major/heavily marketed brands and audiophile/near audiophile grade items at their high end product offerings.
Do you have a budget? Radios cost between $100 and about $500 depending on features for a CD player. Most of them will play MP3s written to a CD in addition to regular CDs. Speakers will run between $50 and $350 or so for a pair. A really nice set of components adequate for most people will maybe run $200 to $350 but sets costing upwards of $1000 are not unheard of. For the rear speakers, I'd say spend no more than $200 for the pair. The front speakers are more important in my opinion. A satellite radio tuner that will be maybe $50 to $100.