I use a paper towel to wipe of the majority of the gunk because OEMs cake that crap on. Then, I use a can of air. Wipe off with a alcohol soaked q-tip until I don't get anything on the tip. Then, can of air again. Apply a quality TIM the proper way. (pea size drop in the middle) Then, clean around the chip with another alcohol soaked q-tip, can of air yet again.
The only reason I do this method is because I use AS-5 and it is conductive. So, I take every precaution necessary. I've done this to my CPU a few times do to changing the Cooler about a billion times. I've also done it with GPUs. same process.
I'd suggest a quality TIM like MX-4 because is basically as good as AS-5, but non-conductive and no cure time. Unless you are doing a delid, then use CLU under the die. Use whatever you want on top.