Personally I'd go for the era of the Berlin Crisis, Bay of Pigs and Cuban Missile Crisis... 1959 - 1962. You've got anything from WW2 kit to the latest in then contemporary military hardware. The US army is hampered by ROCID and most of its infantry still waiting for the M14 and M60. ATGWs are still just in the future and only the US Navy has air to air missiles that mostly work... on some aircraft.
It's less of a technology gap than later and nuclear weapons less devastating (although folk might be less reluctant to toss them about). It was a transitional period all over, so you won't get a much more diverse mix of equipment across the board.
The downside is that some vehicle types might not be available and substitutes are required, like the M113 for the M59, although the M113 was just coming into service.
I'm currently working on TO&Es etc for the 'Cuban Missile War' for my blog... a few days to a week tops and there'll be a ruck of info up there for you.
This year is of course the 50th Anniversary of the Missile Crisis.