I would totally disregard breeds and look for something that is sane, calm and sensible in situations that you will most commonly find yourself in - EG: If you hack a lot, the horse should hack well alone and in company, not hot up in open spaces or when doing fast work and be relatively non spooky, if you want to compete regularly, I would say being good to load is a must, not being clingy to any company that you go with and not being phased by lots of horses in a different environment would all be very important.
There are sane and mad horses in every breed. A friend of mine has an ex-racer who she got off of the track as a 4 yr old (She is now 11) who is the most sane, sensible, sweet, easy to handle horse you could ever imagine. My 4 year old nephew has had a sit on her and she didn't put a hoof wrong. However, there is a lady at the same yard with a TB who is also an ex-racer who is absolutely bonkers. He regularly jumps out of his field, is a lunatic to hack out with, has the tendency to rear in traffic if anything comes too close to him and is liable to spook at his own shadow. I would also exercise caution with natives that have been crossed with either TB or Arab if you want a safe, confidence giving, consistent ride as some of them can have real split personalities - either relaxed and a bit meek and mild or crazy, spooky, fiery, opinioned little beasts. However, they make wonderfully versatile, fun, spirited rides if you have confidence and don't mind knowing that you might not get the same kind of ride that you had yesterday! I would always, always, always look to purchase a nativexTB/Arab purely just because of the brilliant experiences that I've had with them and seem to click with them better than any other breed. My share pony is half WelshxConnie and half Arab and she is absolutely brilliant fun however she is not a 100% safe, confidence giving horse that I would trust with a child or nervous rider as she is sharp, spooky and can try it on if given even half the chance!
Overall though, just look at confidence giving, sane, sensible horses and do not focus on the breed - if you find one of these in a TB or Warmblood or Welsh Section D than that's brilliant! Enjoy and embrace your new friend good luck!
Mine's got Connie in him! Although he's had his mad moments (Bought him at 5) He's so loveable and sensible and starting to grow up! (Now 7!) He is often the lead ringer to take others out on the roads.
Defo stick to your instinct and get something with Connie in it
Of course there are breeds with such temperaments. The Queen's Cleveland Bays cope with a million flag waving folk in the Mall. Not ALL are bomb proof but we breed from stock with know have fantastic temperaments.
Highland Pony I have one who will outface a Combine Harvester!!
Coloured Cobs, a friend purchased a 3 year old who she never had to traffic proof. He was born bomb proof.
Unless you want to do M&M showing then you just need to look at individuals rather than breeds.
Natives ponies can be very intelligent which can make them tricky in some cases to manage. I have New Forest and he is lovely in many way but so bright that it can make things difficult.
I would not buy from a dealer just because they often have not had the horses that long so don't know them that well and they are professional riders so a horse might behave quite differently once being ridden by less experienced rider.
Look at individuals, but if you want to go native then I would recommend a connie, not a welsh. I have both and I adore them both, but my welsh boy is full of himself, quirky and sharp and he is certainly not an exception! My connie on the other hand is the most gentle, kind soul- I am very lucky to own him. He was broken in by a top show producer, and I'm his third home and know his whole history. That, IMO, explains why he is so well behaved- he has been extremely well raised and it does make a difference.