I used a 30M1 carbine for years, out of a tree stand. Then they decided to restrict these handy little rifles and I switched to a 338-08, which is just as well balanced but heavier and has much more substantial recoil.
I used a non restricted M1Carbine for a while and liked it as well.
The bullet I loaded for my rifles was the Speer 308, 110grn, RNSP over 12 grains of 296 and cci small magnum primers, for 1950 fps out of the original 18 inch bbl and a bit more out of the replacement 20 inch bbl.
I tried the 110 grain Varmint Hollow Point but found it damaged to much meat. Before using it on Deer, I tested it in wet magazines and it penetrated quite well.
I needed something that didn't create an exit hole. The Deer I was hunting at the time were mixed in close quarters with other animals and chasing them off their feed. White Tails can be quite aggressive when they aren't afraid or threatened by something they don't fear. That was a one off job though.
Now, I use a M1 carbine that has been fitted with a custom 22in, 1-15 twist Shilen Match bbl with a heavy profile. It's very accurate and more than adequate on Deer out to at least 100 yards.
I don't use it much anymore as I don't have access to the hunting areas I used to enjoy. The farms/ranches are selling off or splitting up and the new houses, along with more people, either create unsafe conditions or push the animals out.
IMHO, the M1 Carbine round will do anything the 357 magum will do and in some cases maybe a bit more.
I tried 125-130 grain bullets in my rifles but they weren't any more effective than the round nose, soft points.