Switch machines are not high current so almost any rotary switch should work. It does need to be Brake before make so it doesn't activate two switches at once. If more than one turnout is going to operate at a position, you will need 2 decks, 3 turnouts require 3 decks.
If you are using slow machines, there are three ways to operate them:
(1) You can use a split transformer with a single common. Each power lead will power a switch in a different direction. Same as above, the maximum number of turnouts operated, decides the number of decks. (This is by far the cheapest way to operate a ladder.)
(2) Another way to do it is to operate relays to throw turnouts. you only need one deck but the paths are controlled by a diode matrix.
Either method is incredibly simple to operate one turn out, but becomes progressively more difficult with the addition of turnouts.
(3) You could operate them with a computer and there are programs available but IO devices get pricy.
Information on all three of the systems are available on the website.
Twin coil machines seem to work well with push buttons and center sprung toggle switches if you have a sufficient power supply to operate the maximum number of switches needed.
Oh, the rotary switches, check at your electronics surplus, new switches are pricy. Don't look for the exact number of positions you need, you don't have to use them all. Many relays allow extra positions to be blocked.
The most important decisions is going to be made at some point when something stops working, which system are you going to be able to fix.
Wow, it looks like I complicated your life.