Dont sand accross the grain, youll leave deep marks/cuts that will be hard to sand out.
There are different types of paper, they have different abrasive material eg aluminium oxide, garnet, carbide. The white aluminium oxide stuff has sterate in it to lubricate and stop it getting clogged good for paint, also good for wood. The carbide stuff is good as it has a very uniform particle/abrasive size(vs others which are a bit of a mix of sizes) this makes the transition from course to smooth papers better as you dont have to sand as much to get the deeper marks from the larger particles out. Ive found some carbide papers leave black marks on wood tho. I wouldnt use garnet, usually its very course.
What you use to hold the paper is important, sanding block, sander, tennis ball for back of bat. Random orbital is good for front face.