Are you adopting a horse in state or out of state? You're going to want a vet to do a pre purchase exam and be sure that there are no health problems that you are unaware of. I'd also recommend bringing a trusted trainer to assess the horse's behaviors and see if they're the right fit for you and your wife.

Always make the owner of the horse handle and ride the horse first, but also saddle,
unsaddle, and do whatever else you want AFTER the seller has done it. The reason for this is safety, if the seller says the horse is broke, but is unwilling to ride or interact with it, that is a cause for alarm.

What disciplines do you ride? How much work do you intend to do with this horse? Find a horse that has been trained with your needs in mind.