Hi,
The 4x50 Watts on your head-unit are in reality hardly 4x22 Watts RMS. Upgrading with an amp will surely result in a big improvement in terms of sound quality. The fact that your original speaker size is a bit on the small side, will not result in a lot of power on the low frequencies. So adding a subwoofer will come in handy. Unless you are able to put bigger speakers in all your doors, then you might be happy to go without a subwoofer.
Full range speakers for your doors are fine. Better results will be achieved with component speakers on the front. Mainly you want to be able to point to separate tweeter directly towards yourself, which is not possible if the tweeter is in your door.
Dampening the noise is surely possible. We used to put asphalt bitumen on the insides of the doors
Pertaining your question on the wattage:
- For door-speakers: 50W RMS onwards is more than loud enough. Many speaker brands use wattages like max or PMPO (peak music power output) which are very very overrated and unrealistic. If you go for the big brands, just look at the RMS rating because this is at least a realistic value.
- For subwoofers: Anything from 200W RMS up to a few thousands of W RMS is possible a good starter set is a 12" subwoofer for 200W RMS. Take into account the space it will need in the back of your car. If you want to go offroading and camping, it becomes a bit of a hassle imho. You can put plugs on it so it becomes removable, but also comes with some limitations.
- For Amplifiers: Always make sure that your amp can deliver/match the RMS wattage of your speakers. There are many options available: 4 channel amps, 2 channel amps, amps which can be bridged, amps with onboard crossovers, etc.. etc...
Chronologically in your case i would take the following route:
1) Look for a good component front speaker set in either the original size that fits, or if possible go for a bigger size. Pioneer, Sony, JBL are good entry level brands. Rockford Fosgate, Kicker, Polk Audio, JL Audio, Focal, Hertz, are more high-end but will set you back a decent buck and are more difficult to find here.
2) Buy a decent 2 channel amp that can power the front speakers. Again Sony, Pioneer, JBL, Alpine, etc will give a good bang for the bucks. If possible go for an amp that has built-in crossovers. You can enable the highpass filter for your front speaker so you can make sure they only play stuff above 80hz. It will result in less rattling in your doors, and anything under 80 hertz will be for your sub anyway
3) Rear speakers: Less important imho. Buy some entry level ones and keep them on the headunit amp.
4) Subwoofer: 10 to 12" is the most chosen option due to power vs size. You can buy an additional amp to power it (2 channel amp that is bridged), or go for these active sub tubes with built-in amp.
I found a shop on SZ that sells Ground Zero stuff. Unfortunately they charge a bit too much like most shops here.
You didn't mention if you want to do this by yourselves or not. It is a nice hobby and if you have some basic knowledge about electricity and removing door panels, it is rather easy to do by yourselves. I made it my hobby many years back and the joy of installing, listening, and fine-tuning it is much higher than getting everything installed by a pro. But that is your choice of course and installing cost here in UAE is not that high.
Good luck !