In the process of putting in a new water heater, I shut off the cold water
at a point much farther from the water heater than its own cold water feed
valve (there seemed to still be a steady trickle through the one right above
the heater, no matter how tightly I turned it off).

The one far away was VERY hard to turn at first (has a lot of that
greenish-white corrosion around the handle, too), but it eventually worked.
however, now there's a steady drip coming out from where the stem goes into
the packing nut (I THINK I have the terminology right here; the drip is
coming out along that little post that the wheel turns).

So am I correct that my first course of action is shutting off the main
water to the house (THAT valve is about 5 feet to the left, after a few
elbows, and it is also pretty caked up with green and white gunk, so I hope
to hell I don't run into the same issue there), removing the wheel, and
looking at that stuff in there? I've looked at the anatomy of valves, and
can't see why removing the wheel would allow the post to slide out. Does
the stem and all the stuff it's attached to just slide out of the whole
thing? Or will it be simpler to loosen the packing nut (that big bolt that
appears to attach the wheel/handle and stem to the big meaty "T" section of
the whole valve assembly) and just put a new wheel/vale assembly in? Or, do
I need to remove that whole big heavy "T" part and solder in a new one?

I apologize for my lack of knowledge here; I've been the muscle on a lot of
carpentry projects, but have nil experience with plumbing. Any help,
advice, etc., would be greatly appreciated. I am a careful, neurotic, and
poor new homeowner.

Thanks for any help, and for reading.