The short, but non-helpful answer is it depends on the saddle and what it was designed for. Especially whether it is english or western, but different variations of saddles inside those two large classes will vary in how they are designed to sit you.
Have you decided on a discipline yet even?
I think you were planning on lessons? If so, relax for now and enjoy them. If not I HIGHLY recommend them. So much of saddle shopping comes from feel that you get from time in the saddle (though professionals can definitely help guide you to finding a saddle that suits your needs and fits when the time comes).
In general you'll want a saddle that supports a correct body position. In general you want a saddle that aids you in sitting such that you can draw a straight line from your ears, through your shoulders, through your hips, and then into your heals. Not all saddles do this for everyone and some won't at all (namely cheaply made ones) which is why it's important to spend some time thinking of fit for both you and the horse. Beyond this though each saddle type is made for something slightly different and will have a slightly different feel and positioning for you. Here's where personal preferance and your discipline decisions come in.
If you decide you want to pleasure/trail ride you'll probably find an all purpose or pleasure seat western saddle ideal (but might not depending on your comfort).
If you decide to do speed events you'll end up with a much lighter saddle with a deeper, tighter fitting seat for more security.
If you want to do dressage you'll be looking for a deeper seated saddle with straighter flaps than if you want to do huntseat/jumping which will have a flatter seat and more forward flaps.
There are in betweens on most all of these, but you can see it's not a simple question of "what fits and what doesn't".
My best suggestion for you right now, since you are so eager to get going, is to go to a good reputable tack store (expensive is fine, you aren't buying yet

) and sit in a bunch of different saddles. This will give you a feel for what you like and don't like and help you narrow your search (which will in turn help us give you advice/suggestions). You'll also hopefully find a knowledgable saddle fitter that will help you determine what sits you correctly and what doesn't, etc.