ok..lets say the bearings inner ring has a diameter of .625". What should the diameter of the shaft be? Should it be exact same size or few thousandths smaller? Or should the shaft diameter be exactly .625" and the inner bearing ring be a few thousandths smaller? As the hole being wore out..I am not sure which hole you are referring to and I can not see how it got wore out...its made of cast iron.
If a person googles bearing fit, interference fit or anything along those lines he will have in front of him more information than the average person ever wanted to know about classification of bearing to shaft fits. Also keep in mind they refer to size difference in tens of thousandths and fractions of microns with a micron being one one thousandth of a mm.
To make a long story short, in this application, we are looking for a light interference fit. In some circles that would be called a "push fit" ie you can push the bearing in or out with your fingers just as you did originally while another may fall off if all it's ducks get aligned just right in a straight row.
So to answer your question, the shaft should be approximately the same diameter as the diameter of the inner bearing race (ring) + or - 0.00001" . The outer race (ring) outside diameters should be approximately the same diameter as the bore they insert into + or - 0.0001. This would be perfect for a push fit when the two are equal temperatures. The difference in the numbers of zeros has to do with difference in diameters.
Keep in mind that a interference fit is referred to a press fit and commonly has 0.0015" - 0.002" / inch of diameter on the tight side and assembled with hydraulic press or other shade tree methods of assembly.
If we had that on our saws dis assembly for repairs would be very difficult.
So a person may wonder why these bearing races (rings) don't spin and ruin everything. Well they can and if the bearings get bad enough where the balls try to mount each other they sometimes do but also realize we have belt tension that is a factor in this equation.
Axial run out - yes with this price of equipment possibly just a little. On space equipment maybe not.