Hi James,
You are unlikely to achieve anything special by trying to find a higher precision bearing for your specific application.
6003Z is probably 6003ZZ – i.e.metal shields on both sides. What you are reading is the marks on one shield only which probably reads 6003Z, along with the makers mark. If Toyo machine, then the makes was probably NMB, NSK, NACHI or similar.
Z = Metal Shield = about a hear line gap between the shield and the inner ring. this allows free running, but can allow a certain amount of dirt in, as Graham said.
RS = Rubber Seal = located in outer ring, with a rubber lip which touches the inner ring, giving better protection against dirt getting in. Greater friction when running, but not really a big issue considering the 'low max speeds' your machine is capable of.
So, you may want to consider 6003-2RS. (2RS means two rubber seals – one on each side).
Pre-Load: as a general rule, radial ball bearings do not like pre-load above a certain point. Angular contact ball bearings do. They are designed for this purpose. So, if you really want to introduce pre-load, look at 7003 B, or 7003 B – 2RS. Arc does not do these, but dig around and you will find. Dimensions for these will be the same as 6003-2RS.
7003 B is 'open' not shielded or sealed. easy to find, but you will need to find some way to seal against dirt ingress. 7003 B – 2RS is sealed, but more difficult to find. Angular Contact ball bearings would be better for your application then the radial ball bearing route.
If you cannot find the angular contact bearings, stay with the standard 6003-2RS bearings. Most Japanese and Chinese origin ones you will find are fine for your application. Depending on where you buy from, they will have a 'C0' or 'C3' raceway clearance. C0 is tigher than C3. Arcs are C0 for this bearing size.
Ketan at ARC.