You might want to try getting an old credit card (I have a blank "sample" card sent by a bank offer...). You can brush some filler on, spread it about VERY EVENLY with the card....scraping it into the grain. That is, scrape "crossgrain". Let it set up for at least two hours, four is better. Sand with 220 grit. Repeat, but sand with 320. Then repeat and sand with 320 or even 400 grit. At this point you're not wetsanding anything, and it takes a bunch of 400grit to get the filler off the body, so scrape it as thin as you can with that plastic, and dont leave any high spots, or you'll need to sand a bunch!
For paper - Home Depot has started carrying a 3m "Sandblaster" paper, that's a premium paper. The claim - "Lasts 3x Longer" is about right on most things. It clogs less too. But - IMPORTANT - you'll need clear the paper VERY frequently anyway, when sanding off the sealer. If you don't, you'll get a hard spot on the sanding block (yes, use a block like the rubber 3m sanding block at Home Depot). That hard spot will "gouge" the wood and give you more to do by way of correcting it. Do yourself a favor and check that paper every few strokes, and use a fingernail or even a small wire brush to get any clogs off the surface of the paper. For 400 grit you might get 2 strokes and have to whack the dust off the paper, then two more... etc... it being so fine, clogs more easily.
The results will be worth the effort. I made sure to take great pains in filling the ash body for the current thinline Tele. I thought the grain was about the same as the Grand Canyon... but after a few fill coats, and much sanding back, it was ready to go.