You have defined the problem correctly, now let’s try to systematically discover the cause(s) and once that is accomplished solutions will become obvious.
Step 1. Play a record that you have not cleaned. Is it quiet? yes or no. If it is noisy then the problem is your stylus.
Step 2. Assuming step 1 revealed no untoward problem, clean your record in your usual way. Is it quiet? yes or no. If it is noisy the problem is your cleaning regimen.
Step 3. Assuming step 2 uncovered that there are problems with your cleaning regimen, they probably are either a) you are not applying sufficient fluid to cover the entire surface of the record, b) you are not allowing sufficient time for the fluid to penetrate (usually 5 full revolutions is adequate), or c) your vacuum timing is off (too little would leave residue, but from your description more likely too much which results in static accumulation). It is not necessary to apply a lot of pressure to the cleaning brush because the bristles are too big to penerate down into the record grooves anyway. The purpose of the brush is to spread the cleaning fluid. The objective is to get a smooth, even film of fluid over the entire surface of the record. If you must err do so on the side of a bit more than necessary. When you have time I highly, highly recommend that you take a look at Neil Antin’s book on record cleaning.

