Almostthere,

Just got my ticket and I plan to purchase a handheld Nav-Comm for back-up

Why nav? For that, you would probably be better served with a handheld GPS.

but it is said that they're useless at altitude without an external antenna
connection.

Useless is too strongly put. But don't expect much more than 5 or 10 miles
range.

What connector do I use (BNC?)

The one that the handheld uses. Some have BNC, some smaller connectors. Or you
use an adaptor to BNC. If you want to use the antennas for the built-in comms,
you will need a special splitter box so that the handheld will not transmit
into the panel comm.

and how do I go about doing this
on rented C172s?

You don't, I'm afraid. That's to say, you don't have control over what's
installed in a rental.

--
Thomas Borchert (EDDH)