All head units have amps built in. No not ALL headunits have built in amps - but for his purposes and budget he is going to have one with a built-in amp
The type of amp you need if you are looking to power all four of your door speakers is a 4-channel amp. Also not entirely true, to be more accurate amps put power to channels not speakers. he would be perfectly fine to get a 2 channel amp because (based on the suggestion from @mylows10; he is only putting power to a front channel and a rear channel and allowing the remaining speakers to be powered by the HU.
Go to crutchfield.com and put in your vehicle and they will tell you what fits. Word!!
Pretty soon you will be spending all your pay checks on car audio... look at my sig. I just started doing car audio this summer haha. I already got $1500+ into my system (not to mention countless hours of install and research) but I also never want to leave my car! yes this is a possibility however if you have a family, like i do, i spend almost nothing on my system, i bought my initial equipment but since then have spent more time trading things and waiting for ridiculously good deals on used equipment.