It all depends on how much you want to spend. The wattage of the basic system is low...probably around 150 watts (max). Your stock system has a small amp behind the headunit to power the stock speakers.
Different people will give different answers. Some upgrade the headunit first. Others upgrade the speakers first. Both will likely produce better sound. For me, i would upgrade BOTH at the same time. However, upgrading both can get expensive.
Some people have gone with changing out the stock speakers to high-efficiency aftermarket speakers (JBL, Infinity, Pioneer). The sound should be a little bit better. But, remember, you're still powering these aftermarket speakers with your stock headunit (weakest link)...so, the improvement is limited. I would not go with the more expensive aftermarket speakers (MB Quart, Polk, Boston Acoustics) because these speakers require a lot of amplifier power.
Just remember this: more power is ALWAYS good. The more power you supply a speaker, the better it sounds (but you do risk blowing it). Also, your system is ONLY be as good as your weakest part!
Another route you can do is to upgrade the headunit. There are many high quality headunit that puts out 50x4 or even 60x4 watts. However, these are MAX power ratings, not average/continuous/RMS ratings. These headunits should be powerful enough to power the high efficiency speakers above. They will likely improve sound of your stock speakers as well (since power is always good). But, again, the improvement will be limited by your stock speakers (weakest link).
These aftermarket headunits have a lot of neat features, including ability to control subwoofer volume (if you install one) and change crossover points.
Good quality aftermarket headunit: Alpine is probably the most popular. Others: Pioneer, Rockford Fosgate, Kenwood, Sony, etc..
There's one headunit that is of very good quality but does not have as much features as above units: NAKAMICHI. They are very simple to operate with only basic features (no MP3). But, they are audiophile-quality headunits. And very expensive!
Other people will upgrade the speakers and also buy a separate amplifier to power them. This kind of upgrade will produce the best sound...however, it will cost $$.
As always, MAKE SURE YOU GO TO A QUALITY AUDIO SHOP. Make sure that you have someone experience to do the job! If you do not, then you risk endless rattles and poor sound from your new sound system! (I learn from experience!)
Hope this helps.