David,
A Disc Doctor brush is a great thing to use in the cleaning process. I use micro fiber cloths as well, as a pad on which to scrub, and as drying cloths. It's important to rinse the record real well (I use R.O. water from the tap).
If you can, acquire a set-up record, such as this one from HiFi News. It REALLY helps, and takes the mystery out of cartridge adjustments. You will hear the difference these adjustments make!