Each English saddle is made to hold your body in the position that is ideal for a specific discipline.
A Dressage saddle is made to hold you in with a deep seat and a longer leg.
A Close Contact saddle is made for jumping, so the seat isn't as deep so you can lift out as you go over the fence. The flap is shorter and more round since you will have a shorter leg then a dressage rider. These days they almost all have knee rolls, which was not the case several years ago.
An All Purpose is a combo of the two, used mainly by eventers. Personally, I don't like them as they are supposed to be a combo, but don't do either discipline particularly well. But most people can't afford a good dressage saddle and a good jumping saddle.
Within those categories you can often choose more options. For example, certain CC brands will offer a deeper or a flatter seat. Certain brands will offer different forwardness of flaps (jumpers like a more forward flap because they often ride with a shorter leg then a hunter) Most brands will offer differing lengths of flaps. And also keep in mind that different brands fit different ways. A regular deep seat of a Delgrange is deeper then a Pessoa but not as deep as an Antares.
If you're going to be doing the hunters I would find a good quality (used, if money is an issue) Close contact with an extra long flap, if that's what you need. Let us know what your price range is and we can give you some good brands!