DO NOT use 'regular' grease. A thin bodied white lithium works well and is easily obtainable.
The use of regular greas will likely cause premature failure. The balls can not circulate properly in the presence of the higher viscosity grease and will 'skid' along the rail causing excess wear on both the rail and the block. Been there, wrecked that as it has been said. Expensive lesson....for my employer, that is.
Using light oil is also an option for loads less than half the recommended maximum for the bearing. Use oil for higher speeds based on the bearing's rated specs. You would want to set it up on a one shot system and lightly oil them every 10-15 minutes of actual use. THis is not a bad idea at all as it would continually purge any crap out of the bearing. You could even automate the lube system. The bearings will run a bit louder but will offer far less resistance than using even the light bodied grease.
ALSO - along the lines of lube - for a machine in a dirty environment, I would strongly recommend plugging the screw holes in the rail. The caps from THK are cheap (.27 USD) and they will keep the crap from sneaking under the seals. Or you could use Bondo or something. You probably do not want to use something that you couldn't remove (epoxy) in case of a problem that would require removing the rail from the structure.
You might also consider plumbing the lube points to be easily accessable. The threads in the blocks suck (in my experience) and have a way of giving out quickly - especially if the blocks have options added to the sealing system - such as additional wipers and scrapers. If you were to put a tube fitting in place then plumb it with plastic tubing to a convenient location it will lessen the chance of destroying the threads in the block and promote good lubrication intervals . Just a thought!