Hi Jules, welcome to the forum!
What I normally do is the gentle dishwashing soap-and-water routine, wherein I lay down a clean lint-free cloth or towel on the bathroom counter, make a mixture of warm water with gentle dishwashing soap in a small bowl, then coat the whole side of the record with a gentle stream of coolish water, lay it down on the towel, dip a new (not used for any other reason) gentle sponge into the soap mixture and begin working the soap through the vinyl IN THE DIRECTION OF THE GROOVES, gently applying pressure around and around a few good times. Then I rinse very well and dry the record, ensuring to blot gently if the label got wet (so the ink doesn't run so much) and do the same for the other side...
I put the record on the platter and spin my turntable at 78RPM (max speed), using my velvet record cleaning brush to dry it for a final time, in case water didn't get out of the grooves in the bathroom. This method has gotten my LPs, 12" singles and 45s SPOTLESS in terms of surface cleanliness, and has reduced crackling on bad LPs significantly. I know what it's like to have to clean really caked-on **** -- many of my old 12" singles I DJ'ed with years ago had dog urine on them from accidents my parents' Malteses had when I was storing my records there after a cross-country move...the urine was actually crystalized on the vinyl, and this soap-and-water method got them LIKE NEW.