Per Factory Service Manual, 75W or 80W - 90 SAE GL5 gear lubricant for normal use. And 80W - 140 SAE Synthetic for towing or other severe use. Using cheap stuff should be okay while breaking in, your choice what you leave in there long term.
Break in procedures should be supplied by the company that made your gears, follow them. If you don't have them, call the company and ask. A good rule of thumb is 10 trips of 20 or 30 minutes driving a different speeds. No hard acceleration, or other high stress use. Let it sit at least an hour between trips to fully cool down. After 300 to 500 miles drain it.
Cool extra trick, if you can get your hands on some high strength magnets put them in the bottom of the case before you seal it up. This will help keep the metal that wears off the gears during the break in out of your bearings. When you chair your oil, clean off the metal particles.
The Chryco 8.25 takes just under 5 pints or 2.5 quarts iirc.