Full seat means that instead of having a patch of leather at the knee area, the leather is all the way up to the crotch and under the seatbone. They provide better stickem.
Most people who ride huntseat do not use them because the tend to ride in two point or half seat and want to be free to reposition their seatbones quckly and easily. However, in dressage or trail riding, if you stay put in the saddle, full seat are really, really nice to have.
I did not look over your listing of material. Don't hvae time right now.
Here's what comes to mind:
Good paddock boots are a must. I swear by Ariats. you get what you pay for. If you need to walk very much, then get the paddock boots with Cobalt Technology. They are not cheap, but will last for years! The non cobalts are also very nice. Go try some on! think $100 to $130
Get your own helmet. Get it fitted to your head. I recommend two brands, but only because these are ones I am familiar with , not because they are the only good ones. For the money, Troxel makes a great product. If you have a more roundish head, then the Troxel will work well for you. Put it on and use the padding to make it tight enough that when you lift the brim it will make your eyebrows go up with it.
If you have a more obloong head , like me, you will like the Tipperary. Very lightweigth and not hot. Both of these brands are around 70 to 80$
If your half chaps fit and you like, then use them.
as for shirts, wear whatever you like.
get a good bra. $45
Get some SSG gloves. They are inexpensive, can by them online and they have good feel. get a bright colore for schooling, so you don't misplace them.\
That's really all you need. If you want to look snazzy, get a vest. THis is one way to dress up a plain shirt, make you look "finished" and not be too hot.