Sounds to me as if you are the sort of person who is going to be OK changing from type to type. You are concerned, you are getting training and are being cautious. All of these are very wise.
I would be much more worried about someone who thought it was easy and not concerned.
So as long as you prepare well, follow checklists etc. you will be OK. Accidents happen when you get complacent, and you don't sound complacent.
I would say that getting experience in different types is good, make sure that you are shown the stall and emergency landing proceedures and characteristics for each type rather than just circuits, You will become a pilot rather than a driver of just one type of aeroplane.