When you say you're currently waiting for your PC to get upgraded, it sounds like that happens fairly soon. I can promise you it won't be a longlasting fun game with only League 1 and up. Better to start with a team in Conference N/S and bite the bullet for now. It'll be a lot faster when the new PC arrives anyway. That way you can have a long, good game.
I have an old PC myself, and am running all of Scotland and England. It went quite allright in the start, but it's getting slower and slower of course. 6th season now, and it can take a good minute to process fixtures. Don't even get me started on transfer windows
I'll pick depth and variety over speed any day of the week.