...and it was suggested the primer be partially? tinted first.

Yeah, unless you're finish coat is something really close to white
[then it doesn't matter].

It's common to tint the primer half-strength [maybe 3/4 if there's a
lot of colorant] of the finish color, and to be on the safe side I'd
wait until you're sure on the finish color before tinting the primer.
There's been at least one instance where the base of the finish paint
or the tints added had an adverse effect on how well the finish coat
covered the primer coat.

As for primer/finish coat combinations, it's not as strict as others
suggest. You can use latex finish coat over any primer, oil or latex.
For oil finish coat I stick with oil primer.

It doesn't matter which primer you use on your walls, but there's no
real reason to go to the trouble and expense of oil primer unless
you're going with oil finish. Trust me, you do not want that. If you
ever wanted to re-paint you'd have to use oil again. And if you wanted
to stop this vicious cycle you'd have to use an oil primer in order to
switch to a latex finish.

Every can has a spread rate or coverage rate on the label, in terms of
square footage. Just assume they're being optimistic and you won't get
quite as much square footage. Especially with new drywall you're going
to use a lot of primer.