I have a stiff shifter, need proper lubricant
 

My shifter is very stiff unfortunately, my dad suggested using some disc brake hi-temp bearing grease because that's all we had around the house. It works alright for a day or two than back to where I started. I have posted a picture below from an Haynes auto repair book, it suggest pouring lubricant into the shift lever extension housing, but doesn't say what kind. Hopefully somebody can help me out with what kind of lubricant I should use. My car also lacks a rubber shift boot which is underneath the leather, I think this would help a little with the smoothness.
http://i769.photobucket.com/albums/x.../lastscan7.jpg

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Gear oil, the same you put into the transmission. Try not to spill, and keep the windows down because it is smelly :)

do you have any recommendations for weight? I have some 80w-90 here at the house but if there's anything better than I definitely want to put that in the car?

That will be fine. 80W-90 is the recommended weight for the transmission in the FSM.