Unlike most other rifles, the grease on the M1 is essential. I had some unfortunate jamming events before I realized that.
Most rifles, if you truly run them hard, and by hard I mean more than 200 rounds in an afternoon, more like 1000 to 1500 or more in a 2 day course of fire, you absolutely need grease on them. AR, AK, M1A, FN, CZ, VZ58, Tavor, Sig/Swiss Arms PE90 - any of the main battle rifles/carbines I've ran hard I've always greased them, and those who haven't invariably have failures, consistently.
There are lots of great products, but basic grease from a hardware shop will work as well.
Congrats on the M1s. I have a few, a standard like yours, a National Match, and a couple Chinese Norincos that are popular here in Canada and inexpensive, have modded them with a lot of USGI parts, one shoots as well as my National Match rifle. SOCOM 16 as well, but I traded it away a while back as I hadn't fired it, and didn't plan to.
Good vids on lube/grease for the M1A, and AR platform IMO.
https://www.youtube.com/watch?v=uG-c_lPB06shttps://www.youtube.com/watch?v=rzVr7JXVxH4