I don't have any experience with wearing face paint at conventions, but I've tried a few types of it at home.
Water-based stuff, yes, this stuff will come right off with sweat. It won't drip off unless you're sweating a lot, but if your face is moist from sweat, it will come right off against even the slightest touch.
Alcohol-based paint is waterproof, but tends to be more expensive, and is harder to get off. Instead of water, you use alcohol to get it off of your skin. The stuff is heavily water/sweat proof. Like seriously, I showered with this stuff on my face, and scrubbed at my face with my hands for a whole minute, and there was still tons of it left all over my face. This stuff is hardcore waterproof.
The brands people usually suggest for water-based are FAB, Snazaroo, and Ben Nye. All of these can be purchased online. I personally would go with FAB.
For alcohol-based, I've only tried ProAiir DIPS.
As for how much you need, you really don't need a whole lot to cover your face. A single normal-sized cake of water-based face paint will let you cover your face at least 15-20 times, but I haven't tested how many exactly. Probably a lot more.
For water-based paints, you can use "sealers" like Ben Nye Final Seal. It won't make the paint waterproof, but it will help make it a little more resistant to smudging and smearing.
Honestly, if you're brand new to face painting (like I was, not too long ago), just look up guides on YouTube. There are plenty of detailed guides on it. It's honestly a lot less complex than it seems. For starting out, just get some water-based paint and experiment with it. It's exactly like watercolor painting: You just get the brush wet, swirl it around on the patch of color, then paint it on your face. Simple.