I was always told not to go to a mirror finish. I was told that having a little bit of the scratches (form the sand paper) is better. Also that when lapping to put the processor and the heat sink with the scratches going in different directions.
I do own a lapping jig that someone built for me. I lap with 400, 600, 800, 1,000, and 1,500 wet dry sand paper. I know that some people go all out and go with 2,000 and then 2,500. There are mixed thoughts of how far fine to go with lapping. Most of the time lapping to 1,500 will drop about 7* on idle.
I never lap a processor until it has run for 3 months.