We've used a variety of components, but I think you'll find that the majority of custom gearboxes in FRC use 1/2" hex shafts and 1.125" OD flanged hex bearings with 20dp hex broached aluminum or steel gears. It's just a super easy, reliable and effective means of transmitting power. Different teams have different preferences as far as plate material, but 1/4" aluminum gearbox plates, even with generous pocketing, provide enough support for just about any FRC application.
Generally, teams get their gearbox plates CNC milled/waterjetted. That being said, simple hole space can be done on a manual mill.
For mechanisms like a climber, I would certainly check out
VEXpro VersaPlanetary gearboxes. They're pretty straightforward to work with and mount directly to CIM, miniCIM, BAG and RS-775Pro motors. That can reduce the complexity of a gear train or eliminates the need all together.
It's also worth checking out the build logs that teams have posted. Many do a great job of explaining the designs as well as the reasoning behind the decisions they make.