My fitting is forward side of rudder tube as far down as possible. It may be a previous owner installation. I believe that what is installed into my tube is a grease fitting "extension" or "adapter." This allows the fitting to be capped when not in use. At grease time, just insert the Zerk. This keeps the Zerk from fouling or corroding over time. And it makes cleaning out the old grease easy.
Note that on the E38, the low Zerk is a few inches below the waterline.
If installing a new fitting (which is easy), I'd look for an epoxy rated for underwater, since the hole will be trickling water.
Regular green marine grease is fine. Any multipurpose grease is probably fine.
The cockpit deck plate covers the connection of the rudder post and top "bearing". Grease applied there eventually wanders down through the bearing (it's really just a bushing). A squirt of 3-in-1 oil doesn't hurt there, either.
It seems to me that the 38 doesn't take much grease in the lower Zerk, perhaps because there's a bushing there. I can only get about 2 ounces in. On other models, like the 32-3, a great deal of grease can be pumped into the rudder tube between top and bottom bushings.
My theory is, grease until it makes a mess, then clean up the mess.
[Apparently later models may not have fittings described in the manual. See:
http://www.ericsonyachts.org/infoexchange/showthread.php?9540-Rudder-Grease-Fittings-on-E-38 ]