My personal goal is to carry one of each - already have the Discover, wishlist is AMEX, Visa, Mastercard (I want Blue Cash, Freedom and Sallie Mae).
I feel that "too many" is when you have so many you have trouble keeping track of what has what on it and which bill is where. That number is going to be different for everybody.
Wanting a mortgage, I'd go ahead and get in the garden now and stay there until you're ready for mortgage rate shopping.
