Capped wires in old switch box--mains power or switch loop?
Short answer, check for continuity between White and Ground.

If you have 120V between White and Black, and White is tied to Ground (check for close to 0 ohms resistance from white to ground), then White is neutral, Black is Hot.

There are some miswired options that may be in play (ie switched neutral), but hopefully this was wired by someone who knows what they are doing.

To answer your other questions:
I believe that measuring hot to neutral on a multimeter should give 120V, correct? 
Correct

What would measuring hot to switched hot give?
120V, assuming that there is a functional light bulb or functioning device plugged into the switched socket.  If not, then you would read 0v, or some floating voltage much less than 120V.