Youtube gameplay really doesn't need HD recording. Same for uploading as that's just pushing bits.
http://help.elgato.com/customer/portal/articles/1020255-what-system-requirements-does-my-computer-need-to-use-elgato-game-capture-hd- doesn't seem to push the envelope here. Maybe you have a PC that can do this now. Share what you have now.
Looking at recording my ps4 gameplay through an elgato hd 60 and uploading to youtube as a hobby, however I'm unsure on what sort of pc ill need. My budget is £500 to £700 thanks.