For that any current or older Mac will suffice. I do that, though not to that extent, on my 2007 iMac and 2009 MBP.
But since YouTube only supports TV aspect ratios like 4:3 and 16:9 a 16:9 display, like the current iMacs, might be best, especially if you stay stationary.
Yesterday I made
this 1280 x 800 pixel screen recording via ScreenFlow (fantastic application), but it looks like this in 720p on YouTube (you have to choose 720p to see, what I mean).
ScreenFlow also offers you to export the recorded movie with the correct settings (.mov using Apple Intermediate Codec for Video and Uncompressed for Sound), but it also offers you to add your own sound files, thus there may be no need for iMovie and that transcoding step.
Feel free to ask more questions, if you don't already.
😉