I can't believe none of the old timers have chimed in on this. The standard for most guys that have been around a while is white lithium grease. I prefer Lubriplate, but CRC also makes a good white lithium. It sticks well, and starting out white you can gauge use by how dirty it gets. You'll also want some kind of shield to prevent spatter, but as you'll see in this video, that's no big deal at all. For bearings I use a drop of light sewing machine oil, or even good old 3in1 Oil.
There's also a method for breaking in gearboxes, some guys use it and some don't, but I'm one that does. I break in my GBs with 50 weight oil, then clean with mineral spirits before final greasing. I've had a couple where the gears where tight and I used a bit of lapping compound to run them in together and that works well, but you can't run that stuff in there for long and you have to thoroughly clean them with spirits to make sure and get all the lapping compound out. Now-a-days that's not really necessary, as gearboxes have advanced quite a bit in the last five years, so a lot of guys no longer bother with the break-in, but I still do it to every set of gearboxes. Those videos are also at my youtube channel.
Hope that helps.