Instead of buying cleaner/lubricant specifically for clippers, just pick up 1/4 gal of diesel fuel from the gas station. Cheaper, and it'll last you all winter season. We just dip the clipper blades (still running) in the diesel and it cools them and cleans off the dirt and hair built up from what you've clipped so far. Also, do long, smooth swipes, not short ones. It'll create less lines. I also like to have a brush on hand to brush off excess hair as I clip. If possible, clip on a warm day so you can bathe right after. :)
"Always be yourself. Unless you can be a unicorn. Then, always be a unicorn."