Say we buy a lot & tear down the existing house, what segment of the
building industry would we approach to build our new home?

Architect or builder.

I'm guessing you
can do anything from retaining an architect to design a one-off masterpiece
(not in our price range)

Price it before you say that, since hiring an architect isn't much
more than building to a pre-designed plan, assuming similar size and
embelishments.

to selecting some builder who has a number of "off
the rack" designs suitable for your needs & budget, probably with some
customizing possibilities ("trim levels" if we were talking cars). For this
latter approach, do you select a "general contractor" who then lines up
framing people, drywall, plumbing/electrical etc?

No, you go to a builder. He is the general contractor.

Sounds like a nightmare
if you don't get someone reliable.

Welcome to the world of home ownership.

Also, what's a ballpark figure for typical suburban home
construction, per sq foot?

Check with local realtors, builders and architechts. My figures here
3,000 miles away won't be accurate.

Jeff