I'd go with the first one for the grease, but that's just me since both would do the job, and as for cleaning you just do as best you can, though if you want to get into it you could also get contact cleaner to start. Get some Q-tips or small foam/sponge pieces and buff the metal clean. If you have a mircro screwdriver set you can wrap a small one with a layer of tissue for the socket side. Apply the grease - which side doesn't matter really since once you slide the connector on it'll get schmeared around. Don't put on too much, and I usually do 2 or 3 connect/disconnect to get the grease all over the contacts.
Then you should be good to go!
Thanks for all the responses. You guys rock.
What do you think about the third product I listed above (I edited the post)? That one looks like the handy little syringe looking thing may make application easier.
EDIT: Just to follow up on this, I bought the third one with the injector. It works great! The syringe thing made application super easy, just inject it into the holes in the male connector of the PSU cable. I am surprised by how much difference this makes in the temp of the cables and connectors. I had no idea this stuff existed. So thanks again for the responses.