Good quality carbon fibre brush (don't use any pressure otherwise your spindle bearing may protest.)
If you have a felt mat, shake dust out of it before and after an LP listening session.
Check whether 'crackling', pops etc happen more when you are using the lid if you have one.
Only ever use a clean, slightly dampened, soft cloth to clean a lid. (Those blue 'chamois' style cloths to clean LCD screens are ok but only moisten slightly with a spray or two of water.) Buffing a lid with dry dusters etc. is guaranteed to raise static.
Ensure you are tracking at (or very near) the top of the recommended tracking force/weight range given by the cartridge manufacturer. Make sure this is accurate by use of a Shure or Ortofon stylus tracking force gauge. Obviously the anti-skate/bias should be set to the same number as the tracking weight.
Only use fluid/paste/facemask solutions with extreme caution and test first on your least favourite record first. (Or buy some 20p record in a charity shop to test it on before using on cherished rarities!)
The only exception to the above is a Keith Monks cleaning machine (my local record shop has one and charges a quid a side). KM cleaning is totally safe when done properly. There are other similar cleaning systems around from £300 up to many £Thousands but that is not really appropriate unless your turntable and LP collection merit such an investment.
Good quality inner sleeves as recommended already.
Good quality, nude elliptical, fine-line, Gyger (etc) stylus profiles dig a bit deeper and, on a good arm/turntable, will force some irritant noises into the background but there are limits to this.
Extremely unlikely this one, but if your listening area has very low humidity, this can effect static build up. So put some potted plants in the room and keep them well watered and keep the room well ventilated.