After using cast bullets in at least thirty US-made .30-caliber rifles, dating from 1896 to about last year, I can tell you this:
In the vast majority of my .30-caliber experiments, the best results were obtained (WITH CAST BULLETS, remember) when the bullets were sized at .311"....that is...three-one-one. The normal "rules" for jacketed bullets DO NOT APPLY to cast bullets. An occasional rifle might want another diameter, but .311 will work with about 98% of them. This is based on loading upwards of 5000 cast-bullet rifle rounds per year, and many of those are .30-caliber of one sort or another.
I've been playing the cast bullet game for almost forty years, and have learned a few things over that time. .311" is where you want to start!
For an in-depth education on bullet-casting, and loading the resulting bullets, go to:
www.castboolits.gunloads.com
and we'll be mighty glad to make you welcome. It's a fine bunch of folks, and very tolerant of newcomers, who are viewed as the future of our hobby. We also have a LOT of fun in the bargain. Maybe use the same "handle" so we know who you are? Ask exactly the same question there, and see what the laddies have to say.
The press you have will indeed work with the Lee .311 sizing die, no problem. It will seat the gaschecks, too. Later on, you may want to move to more-elaborate equipment, but for now you're doing fine. I'll be looking for you to appear over there, Lucky....