I've dealt with a handful of aggressive horses over the years, they aren't fun and take intense work to deal with. My personal horse was one of them, not his fault, he was turned into that horse. My hubby was sure he'd be the one to end me or at least do serious damage, thankfully not. He went from being one that would bite, kick, charge, rear & strike to now being a good citizen, big baby on the ground and very quiet & willing under saddle. At this point I even have hope he may become a kid's horse many miles & wet saddle pads down the road. I'd not EVER recommend going that route to anyone, it's hard work not for the faint of heart or inexperienced to overcome major aggression issues.
I think many new owners get taken in by a pretty package and hope to love it into wanting to be a willing partner, that doesn't work.
Biggest recommendation, find someone knowledgeable to evaluate prospective horses with you. Someone who doesn't have a dog in the fight so to speak and can look at a horse objectively.
Don't settle on the first one you see or the second. It's like finding a perfect pair of jeans, you might try on 20 pairs before you find the one pair that fits you perfectly.
Don't ever take an owner's word on something. Find out for yourself if that animal is what it's advertised to be. I've found more often than not that they aren't. What one person considers broke and what I consider broke are often vast distances apart.
High price tag doesn't always equal good.
Free or cheap generally doesn't equal good.
Look into bloodlines and history when possible, if dam & sire were hotheads, chances are the offspring will be too. Don't buy one bred to be a cutter when you want a jumper or vice versa. Look for one that is bred to do what you plan to do with it. Trying to conform a horse into something it wasn't meant to be is like trying to fit a square peg in a round hole.
Ask for medical history & vet records, look for sedative purchases, x-rays, etc. Never skip a PPE.
Ask for name & number of the person that started/trained that animal under saddle, call, ask what they were like to work with. You'll generally get an unbiased opinion when that horse isn't on the payroll anymore.
Ask for reference from the farrier. Find out what that horse is like to deal with from their point of view.
If a horse is already brought in and tacked waiting on you, red flag. I walk when that happens. I want to catch that horse myself and go through the whole routine that I'd do myself upon purchase. If it isn't tacked, look for sweat marks, be sure they've not worked the snot out of it first.
That's what comes to mind now, there's much more but who wants to read a novel?