Most woodworking tools are fairly priced, so pick one in your budget and you
should be okay. As someone said, variable speed in a handheld is not
necessary, but doesn't hurt.

As long as it hasn't been dropped on the floor, a used router should be
fine; good luck finding one.

A PC router, such as what other people have suggested, will save you a
couple dollars if the jig came with a template guide that fits only PC
routers.