Of course my first vote is QH, but that's my thing :) I agree with other posters, don't worry about breed. Judge each individual horse, make a list of what you want, things that are deal breakers -for me my big deal breaker is cribbing, I like my fence too much to be replacing posts for a cribber or wind sucker not to mention the teeth problems & other health issues that can stem from it.
I agree with looking for something with some age on it, but don't forego a thorough PPE by a reputable vet. Ask the current owner to give their vet permission to release full medical records for your viewing, if they aren't willing RUN the other way.
I always tell folks I help find beginner horses, NEVER ride any horse that the owner won't ride first.
It's always a good idea to take someone knowledgable with you, so you have eyes on the ground to watch for any signs of unsoundness while being lunged or ridden.
Take your time, don't rush. The last beginner horse I found for a student was the 17th horse we looked at.
Life is like a camera. Focus on what's important, Capture the good times, Develop from the negatives and if things don't work out, Take another shot.