Absolutely HAS to be sane, sound, and well-put-together - I won't compromise on those. If it rears, I won't touch it, because I ride mostly side-saddle and if it goes over backwards I'll go with it, but I don't mind the odd buck here and there. Kicking/biting is also a deal-breaker. Straight, ground-covering (but not high) action is a must, because that's how horses stay sound.
It needs to be at least six, because young horses don't have the muscle to carry a side-saddle, and I'd prefer to have something with a good record out hunting. 15.1-16.2hh is my target height (15.1hh for a lightweight cob; 15.2hh for a small hunter; 16.0-16.2hh for a lightweight hunter), but I'd consider something bigger (in height or in weight-carrying ability) if it was mannerly. I'd prefer not to buy something smaller because the family's current 13.1hh built-like-a-tank Highland (who will be in the family for life) is rather on the small side for me nowadays (we bought him when I was 9; I am now 20 and quite a lot taller).
I generally prefer mares to geldings, but I'd have either (nowhere to keep a stallion), and I'd really like a dark solid colour, but I'd take a grey if it ticked the boxes and we clicked (I wouldn't have a coloured horse because the only ones I like are traditional cobs, and I don't want a horse with full feather because it's all clay round here and feathered legs are so prone to mud-fever on clay).
Plus, obviously, I need to be able to actually afford the horse in question. That's quite important.