I'm tempted to caution you away from thoroughbreds, ESPECIALLY those off the track. An OTTB needs a very experienced rider, or a very capable rider with very experienced guidance. Very experienced = has worked with and trained many horses from the very start, and has worked with horses that need retraining. A very experienced person has the knowledge and confidence to solve any problems the horse might throw their way. That said I know (and have worked with) some exceptionally quiet TB's, one that was quieter and more reliable than my old standardbred. But even she had her 'moments' so trust me, unless you've got a good coach, a TB isn't a good idea for a first horse.
QH's are awesome horses, Mum had one and he was lovely. Jet Boom lines. He was her first horse and she got him when he was a yearling - NOT a good move by the way, but because the horse was so exceptional, it turned out ok. Draft types are awesome too, but if crossed with TB or Arab can be difficult. Depends on the horse.
I agree with those who are saying don't go for a single breed in particular, but be aware that some breeds, particularly the ones with reputations for being 'hot', might be perfectly behaved 90% of the time and then difficult 10%. That 10% is enough to destroy your confidence if you can't handle it. No matter how awesome/quiet/reliable your horse is, I can guarantee you'll need some help with it at some stage.
I have an anglo-arab, and I almost passed over him because of the Arab breeding (not a fan of them as a general rule), but he turned out to be the most awesome horse I've ever had. But he makes me RIDE and ride properly, because if I'm not doing it right, he doesn't respond. He can't stand an unbalanced rider and will throw in the odd small buck. You have to ride him forward and LET him go forward (problematic for me because I've come off him from a gallop so it's kind of scary, but I'm getting there) because if you don't LET him go forward, he'll pull like a steam train and there's no stopping him. If you don't LET him go forward, it becomes a battle of strength, not the beautiful harmony it could be.
I thought I could do it all without a coach, trust me everyone does at some point, but I was so wrong. Now I have an amazing coach who I see weekly, and HE is the one who made me realise what I was doing, and exactly how MUCH was my fault (ie, everything).
Whatever horse you get, make sure you have a good coach lined up for you to ride under on a regular basis, because that horse will try you out, and you may need that coach to help you stay on top (literally and figuratively).
Oh, also? Green + green CAN work, but more often than not, it doesn't, and the rider gets hurt, and the horse gets branded as dangerous. You ideally want something 10+ with a lot of miles under saddle. Green + teen doesn't work that well either, I have a friend who's had heaps of green horses but because she's just hitting teenage years she keeps saying her little 4yo TB is being naughty when the poor mare's just being confused. I was BOTH when I got my standie, so I know from personal experience that it just isn't a good idea.
Would I do it all over again? Yeah, I would, except I wouldn't take the risk of buying a horse with scarred knees. That horse taught me so much. The knee injury came back to bite us though.
And never, EVER make the decision just based on what your heart wants. Don't buy a horse your heart doesn't want, but don't buy a horse that your head isn't sure about. I made a 'heart' purchase and it went horribly wrong. It's really hard to tell your heart no, but trust me, it's worth it.
Edit; wow, sorry it's so long!! This is something I'm really passionate about. I hate seeing people struggling with the wrong horse because I know how bad it sucks, and I know what it's like to have your confidence destroyed. I don't want that to happen to you, or anyone.