J B,
In theory,The best patched bullet core is .01 over your bore diameter. Most 30'06 bores are .300,so I would start with a core diameter of .301.
That works best for my 30/30.
My 30/40 Krag,on the other hand,will not shoot that bullet. My best accuracy is with a Lyman #311041 bullet sized to .308,and then sized again to .313,after patching. This sizes the core to about .307.
Good luck
Frank