SAFE
Unless your going to be showing in Breed shows-where all the horses in that particular show must be registered within that breed registery. Just look for safe. Then look at what type of riding you will be doing most-You would not look for a draft horse to ride endurance or an arabian to pull a plow. Then where is it going to live if @ home you want to look for low maintanance-No major health/lameness issues and doesn't need regular riding by trainer to stay safe, Also if at home do you have a trailer should it need to go to a vets or trail ride or showing. One of the best places to look is thru your local riding or 4-H clubs as those ponies/horses have been outgrown by their previous riders. Take into account your daughters size something on the thin size she may outgrow and know her confidence level she may want a more kick along type over the eager to go. There are huge possibilities not only on your purebreds but now everyone has gotten into cross breeding and createing new registeries. So if you are drawn to a few different breeds that may be a possible cross someones already created. The best pony I've ever had 38 yrs old today came from my blacksmith, taught his boys how to ride and has taught both my girls[10 yr differnce btwn them] She was a "take your best guess" breed. Sometimes those are the best yet.