Good idea! I've been a hobbyist level woodworker for over 10 years. I'll just throw out some unsolicited advice. I'll be happy to try and answer any questions.
Plywood from HD, Lowes, etc. generally sucks. You can find some decent sheets there, but I always have to sift through the entire pile and I'm lucky to get a couple nice sheets. Try to get your plywood from a local cabinet builder place, woodworking supply, etc. Baltic birch is the best ply, but more expensive and hard to find.
After cutting plywood, the sides are very rough. I put wood filler on all the sides then sand it smooth. I sand all surfaces up to 320 grit. For a pickguard, I'd definitely round over the top edges, but probably not around the pickups.
My first finishing step is to wipe on a dye. I use Rit clothing dye. The dye is cheap, won't conceal the wood grain, easy to apply and reduces blotching. The dye is water based and it'll raise the wood grain, so lightly sand with 320 grit after dying. Unfortunately, the color of the dye is usually not great, so next I wipe on a thin layer of stain, then quickly wipe off. When the stain no longer has a strong smell (24-48 hours) you can apply the top coat finish. Finishes can be very confusing due to marketing crap. For a pickguard I'd use polyurethane (it's the most durable finish). Wipe-on poly is easier to apply than brush-on. Wait at least 12 hours after the first poly coat then *very* lightly sand with 600 - 1000 grit to remove dust nibs. Clean off sanding dust and apply another coat. Repeat 3-4 times.
Other finishing options (in order of my preference) are spray-on lacquer, shellac, or just an oil - like danish oil or BLO (boiled linseed oil).
