I'd suggest you shop around first.
A well setup and matched 2-way can do pretty well on its own but compared to the much more expensive well setup 3-way, it'll be outclassed la. 3-ways can be a pain in the ass to tune in terms of speaker positioning, crossover points (if not using passive) and placement of the speakers themselves if you drive a small car.
Personally I'd just stick with 2-way first.
Also I'd suggest the following : Sound proof doors, custom door panel, 2-way components powered by a class AB amp, sub powered by a class AB monoblock.
And depending on the brand of the components, you'll be surprised what a high end 2-way can do. The 2-way highest end Sinfoni components will outshine a lot of brands you'll come across. Heck even my Dynaudio 240 MKII will do better than most brands out there. But the way these two sound are like day and night and depending on the amp you use to power them, they may or may not be to your liking.
Instead of going to shops, you should mix around with ICErs and test try their cars and their speakers. Then only decide which one makes you happy, find out who the installer is and go to that person and ask for the same or similar setup.