I'd have to ask first, in what type of application do you intend to use these bearings? Most bearings are designed for particular applications and appropriate bearing lubricants specified for the mechanical application.
The NLGI, National Lubricating Grease Institute, publishes several handbooks which may be of help, but I would first determine the following questions:
1. Is the bearing used for high-speed or slow speed applications?
2. Is the bearing used in a specific unusually high heat situation (examples: coffee roasters, boilers, incinerators)?
3. What does the manufacturer of the end-product specify for a lubricant?
Finally, with the info above, you might look at some of the high technology synthetic greases out there, many of which far exceed petroleum-based pressure applications,etc.
For oiled bearings, you might want to consider a top-line synthetic oil as well.