I bought a 3 inch phase II vise from travers for $65 at NAMES.
It fits my rockwell mill very well. I tried a 4 inch kurt and it
was just too big.

Is a swivel base worth the extra cost? Is it rigid enough?

That price included the swivel base! It may have been a NAMES show
special price though. I have not used the swivel base yet so I
do not know how rigid it will be.