Yes, definitely opt for the swivel lock! I can lock both casters on 1 side and push the gantry solo from the other side. I can't imagine trying to make the gantry go where I wanted without the swivel locks, it would be a circus.
Size the diameter for your surface. Generally larger is better. Unless your surface is relatively smooth, I'd go 8" minimum.
I have nylon wheels and they've worked well for me. That decision was partially based on storing the crane outdoors and budget.