Matt, rotax doesn’t make a 6-speed kart motor. All rotax’s are single speed with the exception of the DD2, which is quite rare and has 2 speeds.
My Skip Barber instructor said that the next step up from a shifter kart is an indy car, so you’re probably not going to want to start with a shifter. Tell us what your budget is for a motor and we’ll try to point you in the right direction. You have a lot of options and you’ve got a good chassis to start with. Where do you plan to race it?