I don't know the specific paper weight, but our stickers are paper based, with a PSA adhesive backing. They come with a crack and peel wax paper on the back. The front is sprayed over with a thin layer of uv cured finish, but they aren't waterproof.
I had to make a few mock up custom labels a couple of times and I used some sample paper stock from our printer. From what I understand, they can jam up the rollers in laser printers. The heat generated from applying the toner makes the adhesive leak from the sides and stick to the rollers. I only had to run a few sheets, so I chanced it and ran it through the printer.
If you want to run something on your home printer, I'm sure you'll be fine. I would imagine you can get good results by using some low sheen photograph paper. It's heavier stock than plain printer paper, which looks classier, as a label. You will have to experiment with coatings, but I think spray can laquer will do the trick. Couple things to be careful of. The solvents in the laquer may cause the ink to bleed and/or the shrinking laquer may cause the label to curl. If bleeding is a problem, you can try doing what's called a tack coat. Before spraying the actual top coat on the label, give it a really thin coat and let that dry. The idea is to create a thin enough layer that won't bleed the ink. When it's dry, it should provide enough protection from the subsequent coat, preventing or minimizing the bleeding effect. We use this trick when people have a famous signature on their uke and want it sprayed over. Even fully cured Sharpie ink bleeds, when shot directly over. If you can find polyurethane spray can laquer in your area, even better. Poly chemically cures, opposed to nitrocellulose. The tack coat will provide better protection with the resistance of the poly. To fight the curling, you can either live with it, or make the label oversized and tack it down to a flat surface. Let the spray dry for a day or so and then untack it and cut off the excess. It'll probably have some spring back, but it should be better than letting it sit without reinforcement.
As for the sticking application, 3M makes a variety of mounting adhesives. I can't remember the name, but I do buy this stuff in a can, designed for affixing labels and such. It's availa
X-C20at most hardware stores.