It's normal for the gauge to go to hot when you turn off the engine, no cause for alarm.

My '66 never had an overflow bottle -- I think that started in '67. It doesn't run any hotter or cooler with one.

If the radiator is beat up, you should consider having it recored (if you can find a shop that still does stuff like that). Note, though, that the original core is dense, with lots of closely spaced fins. You want another core like that, not a generic one with fewer fins.

I lived in the San Fernando Valley for 10 years, and never had the car overheat.