not necessarily. On modern chassis, 30mm seems to be a sweet spot, like James said. 32 may end up being too stiff and coupled with higher weight of the driver create way too much load and hop like a bunny. If this is your first kart, get a good used 30mm.
If you find a chassis that has front brakes and it’s a good deal, get it anyways. You can run it with all brakes, move the bias all the way to the rear or deactivate the fronts altogether (takes 1 minute) if you want to run rears only or race local/club. With the added bonus that in the future you can use it for a shifter, should you decide to try that route.
Stick to a major brand common in your area and you’ll be happy!