Mint Mate is user friendly, well put together and has a helpful community so I would try to get it to work first. I would not expect Cinnamon to work well on an older machine.
If it does not work, you could look at:
Fedora XFCE and LXDE spins
Debian + E17
I use Fedora XFCE on my oldest PC and it works fine on a processor one generation more recent than a P4 (forgotten what its called!).
They offer different trade-offs - user friendly vs effciency vs learning curve vs community vs repository size.
As you say you are a Lnux newbie repository = app store.