Just found this picture from an old ebay listing. Looks like mines an exact clone of a wissota E67
Yours isn't a clone; it was actually made by Wissota for Wilton. The "W6-9" in the serial number space on the nameplate is probably a manufacturing code for Wissota. Milwaukee did a W-code thing similar to that on the Milwaukee-badged grinders that were actually made for them by Wissota.
Even though they stopped making bench grinders a few years ago, Wissota still supplies parts and support for many of the grinder models they made.
The vibration is likely at least partially due to an unbalanced wire wheel or the grinding wheel, but changing the bearings is a good idea anyway and easy to do. You'll still need to deal with the balance problem to get rid of the vibration.
If you're going to keep a wire wheel on one side, I'd suggest not worrying about the missing side cover and tool rest. Using a wire wheel with a tool rest and completely enclosed wheel isn't the best idea, nor does it give you maximum flexibility in the use of the wire wheel.