Don't worry about stalling. Your average training type by nature of its design is usually not fully stalled during a 'full stall' anyway - the wing tips are often still flying. This makes them have very benign stall characteristics (which is one of the reasons they're chosen for training!)
Try the PA28 for instance. Its stall characteristics are so benign as to make it a real non-event. Get into a fully developed stall and it just happily mushes down at about 1,000 fpm. No wing drop, no surprises, nothing really. The C172 is also pretty benign. The AA5 favoured by Cabair school can be a bit more of a handful but is fine as long as you control any wing-drop with the rudder (without picking up the wing).
Now, if you want more fun during your PPL training, ask your instructor to do the optional spin training (as long as your type is cleared for them).