A dab'll do ya. Marine grease is great, a pea size amount is enough or even more than enough for most small metal gear and part lubrication. For plastic gears, use white lithium grease. Funny, I can smell marine grease in my head just thinking about it.I use marine grease on the joints and moving parts of my wiper motor animatronics. It's more water resistant than regular grease. Honestly, I had a tube of it from back in my boating and fishing days, tried it on a prop and it seemed to work well so I stuck with it. Not sure how well it would work on plastic gears though.
A well stocked RC hobby shop has all kinds of things that cross over into prop fixing/hacking/building. Good, high capacity, small rechargeable batteries are indispensible, plus paints, tools, electronic parts, etc. One year I made an RC car dressed like a spider that leapt out of the bushes at 65 mph. My Dad had so much fun operating that one!then likely some sort of grease from a hobby shop specifically designed for plastics would be ideal
Specific brand? Doesn't matter. They're all the same that are chemically the same. Get the cheapest of the type you end up selecting. Auto parts shops like NAPA are super helpful, too. If you explain to the counter guy/gal what you're doing with it, they'll point you in the right direction.