The original mil-spec grease was Lubriplate 130-A grease:
The 130-A would be used in normal environments, the 130-AA would be used in arctic conditions. As NLGI numbers go up, the grease base becomes thicker. NLGI 00 grease can be poured at room temperatures - it's about like tar in consistency.
NLGI 2 grease is the most common consistency you'd see on cars, trucks and heavy equipment lube specs. The most common base for NLGI 2 greases is lithium, which you could also use for greasing the Garand-type rifles if your rifle sees light use in favorable conditions. The 130-A/AA grease is a calcium based grease, and calcium-based greases are very good at repelling water.