First find out what the max and min sizes are for that bike.

Swapping tires is just annoying enough that you won't do it much.
It's a lot easier to swap wheels. Use the wheels off the old bike for the big tires.
And the new ones for the small tires.

I'm a big fan of the Vittoria Randonneur tires. I have the Rando Hyper, and want to try
the Rando Pro when these wear out. They ain't cheap, but they are worth it.