no joke, you definitely need to search around...
and the comment about 50x4 written on the front of the radio meaning each speaker gets 50 watts...that's not all the info you need.
If it says 50x4 on the front, this is most likely PEAK power. Peak power is the most power a speaker will get in a short "burst" of highs or low notes. The amp in the headunit cannot provide this 50watts continously. PEAK power is arguable. More importantly, you should go by RMS power. RMS is the amount of continous power the headunit's amp can provide.
For example, take a Clarion radio and an Alpine. Both may list 50x4, but the Alpine could be much louder. Turns out a Clarion radio I purchased a couple of years ago had an RMS of 17x4. This was not loud at all compared to the Alpine's 26x4 RMS. I would look for mid to high 20s at the very least for your RMS power rating.
Oh yeah, and make sure you get an aux input- this will save you much trouble when integrating the audio from your carpc.
if you get a proper power supply such as an Opus, Carnetix, or M1-ATX, you won't need to lug around a second battery. These power supply not only provide 12V power with the AC conversion, they also regulate the power. Car power is a very rough environment for something as sensitive as a computer. Also, in these power supplies are startup and shutdown controllers. Not to mention that some of these, such as my M1-ATX, will monitor your battery level and cutoff power to the PC if the voltage drops below a certain level, say 11V.