"...125 grain .303 bullets will work..." They won't be .303", but neither is a .303 British or 7.62 x 39. The latter uses 123 or 125 grain bullets, normally, so you're all set.
If you're shooting a semi-auto, you must full length resize every time. And watch the case lengths and loaded cartridge OAL.
Hornady's 123 grain SP or Sierra's 125 grain SP Pro-Hunter will do nicely.
Load data is listed as 7.62 x 39 Russian on Hodgdon's site. Occasionally the 7.62 Soviet. Some manuals call the 7.62 x 54R a 7.62 Russian too. Not the same thing.