That does look a lot like a grinding spindle, or some other sort of low load high RPM spindle. The best way to rate the one your going to rebuild would be to not exceed the RPM rating for the bearings you will install. I would think 10K would be just fine and should suit your needs.
I wouldn't put too much load on a spindle like that, they generally were never made for high torque milling ect. The shafts are thinner, the bearing placement isn't optimal and the bearings are probably ridgid and not meant for axial thrust loads.
As far as lubrication, most grinders are either greased and "sealed for life" to where the bearing was greased on assembly and no further lubrication is required for the life of the bearings. The other is an oil/air lubrication which those lube units can be expensive, but they basically just put a low PSI flow of air into the bearings with a slight mist of oil, too much oil and the spindle can get hot and the oil will tend to puddle inside. Not enough and you can guess what happens. You could just use an air tool air dryer and oiler, should work for your app, just use .125" nylon tubing to feed the bearing supply and try to figure a way to regulate the oil flow. Too much oil is better than not enough! And 20 psi is sufficient.
Hope this helps,