The below is all just my personal opinion.
There’s something going on in unbelievable story’s back end, his pelvis looks like it has a bit of a twist. Look at the shot from behind, he’s standing square but his hips are not even. The left hip and tuber sacrale is noticeably lower than those on the right. There is more muscle development over the right hip and wastage over the left so there’s possibly a compensation there. His tail looks kind of corked to one side. In the video of him under saddle he’s ridden largely on the right rein so you can’t really assess how he moves on the left rein which would probably be the more difficult direction for him. In every canter photo he’s chosen to canter on the right lead even when it appears he’s going left. He’s also incredibly straight through the stifle and hock. I’d steer well clear of this one, I think that nearside hind has issues that would be more visible on the left rein.
Nosey has a nice big bottom but those long pasterns on his front feet will be a weakness particularly as you’re wanting to jump him, one day they will probably give out. He trots with a bit of a daisy cutter type movement, I wonder what the injury was and what they saw on his xrays. Shame as he looks sweet.
Convict is cute but whether removed knee fragments can cause ongoing issues or make them unsuitable for jumping I don’t know.
All of these horses have problems of varying severity, whether they’re dealbreakers or not is up to you. Yes they’re all cheap horses but if you have no space for retiring a horse if/when it goes unsound, or no $$ for lameness workup, the purchase price doesn’t really matter as you’ll be stuck with a horse you can’t find a home for. Me personally I wouldn’t take an possibly-unsound horse even if I was given it free but that’s because I have nowhere to retire them so I won’t take on the risk.
Resiliency if it were me, I’d want his back xrayed to look at whether he has kissing spine or not, and his feet to see if the bad angles have caused any arthritic changes. If they’re clean he’d probably be my pick out of the list.