What association is the mare registered with? Most other WB registries will let you submit the mare’s papers w/ 4-5 -gen pedigree and will give you preliminary idea of mare would be eligible for approval with them.
I strongly recommend pursuing a course that results in a WB-registered foal. Breeding for yourself is fine, but those papers make a big difference if your life situation changes, the horse gets hurt and needs a broodmare job, or is just isn’t something you want to ride (too quirky, or spooky, or limited in scope, or whatever)
I would not recommend Sir Caletto. He’s gorgeous, and has a jump to die for. But there’s a reason you don’t see a ton of his offspring doing hunters. Many are difficult, and most end up a little too spicy for the hunters. I had a SC colt I bought at 1-week-old. He spent his first few years with a good pro trainer who showed him on the line, but he was so quirky to start, she actually had me send him to a cowboy for a few months before going back to her. This was a pro who’s well known for bring young horses up the ranks to legit and successful AO/Performance hunters and Big Eq horses. Sadly I lost the gelding to severe wobblers a year later. (another reason I would not use SC, though the issue may have come from the dam, or just a one-off bad-luck thing)
R line hanoverians are well known for great, ammy-suitable temperaments, and many make very nice hunters. I’ve had several and all were naturally quiet and had great brains.
A lot of holsteiner lines © are known for really good jumps (though many aren’t great hunter movers) so that might a be a good place to start. Many stallions are approved for multiple registries, so I recommend figuring out what registry you’ll register the foal with, then look at their list of approved stallions. Narrow the list by looking at height, their bloodlines, and conformation/type. Then talk to the owners of the stallions you like. Most are good about telling you what things their boys pass along. Look at old COTH threads about those stallions. And check out internet classifieds for horses with that sire.
Also, expect the whole thing to cost a lot more than you expect. This year’s foal was conceived on the first try, and delivery was textbook. He’s perfect. But last year I lost the foal and almost lost the mare, who needed an emergency C-section. This year, I’ve tried 5x times to breed (2 mares) and still don’t have even one mare pregnant. That all adds up REALLY fast with nothing to show for it.