Your amount of forwardness while posting or in half seat should be dictated by the saddle you use, pretty much. All saddles have a balance point that is created by the position of the stirrup bars and how the saddle rides on the back of the hrose and such. You can experiment with how far upright or backward you can stand in the stirrups without falling backward. Just in front of that will be the balance point. As your legs and core get stronger, you can ride really close to the balance point. If you are new to this kind of riding or lack the physical strength of the leg, you will have to compensate by leaning further forward.
You are lucky to be able to try all these different things on good, ol' Gidget. She's a gem!