I know of a woman who didn't ever ride until she was 57 and then she decided to start...riding saddleseat on Saddlebreds in the show ring...after lessons of course but she did very well indeed.
While you might need to drop some more pounds, you should go ahead and find a barn to work with you on ground matters. Leading, feeding, grooming and tacking up. Good exercise for you too, and may help with weight loss too.
You can gain a lot by getting ground work right now. Learning how to do the things you will need to know when you begin riding will help. Your attitude, which will be so important when riding and handling horses, your movements, your handling of horses will be much better.
As for your height, I would think anything 15.2 and up...but much depends too on where your length is. Many people your height have most of their length in their legs, others carry more length from crotch up. That does affect balance also, as will your weight.
Go to each of the barns and ask about maybe doing groundwork and see too if they can use someone to help clean stalls while you are there, or even clean tack or water buckets. You will get more relaxed the more you are around horses doing that.
You will really enjoy horses I think.
As for a horse to ride/own, I would look at something with good bone, that is sized to carry you well, and a kind horse to boot.
Horses make me a better person.