TB's seem to be the eventer's horse of choice, They have the atheletic ability and stamina to do all 3 phases of the competition. Most are brave and will try their hearts out for you. My personal 2nd choice would be a Connamara, but they're a little hard to find. Whatever the breed, I think it's important to have a horse that you can have a strong bond with.
TB's are typically what you find in your average eventer barn. I don't mind TBs and I certainly don't deny that most are excellent eventers, but I've always loved baroque horses (Andalusians, Lipizzaners, Fresians, etc. Though the latter two will be out of most peoples price ranges.). Andalusians have great bone structure, are very intelligent, and have the heart, stamina, and will to do the job. They'll handle anything you throw at them, including eventing.
I'm currently on the hunt for a pony eventer, and my main concerns are for them to have basic correct conformation with willing temperaments. It's hard to judge a horse completely on his suitability for a discipline just by a conformation shot, and there are also many horses that compete with what many people consider to be "major flaws".
It also depends on what level you hope to compete. For BN, really anything can do it. Novice, you have to be pickier because the demands are higher, but still most athletic horses have no problem jumping a 3' course. Buying anything unproven for anything above training level IMO is when you start taking a gamble, (mostly for the cross country) but hopefully if you wanted a prospect that could take you there and/or higher hopefully you'd have a trainer to help you first hand.
TBs are great eventers, but I'm not sure they're ideal for the higher levels solely for the dressage. Conformationally TBs are bred for speed and endurance, and aren't typically purchased as high level dressage mounts. There are always exceptions, but just saying.
TBs and Arab crosses are my choice. I like how compact the Arab crosses are but a lot of it is hit and miss. I know a lot of backyard bred Arab crosses with huge physical flaws that would limit their ability.
3/4 TB 1/4 draft are good. That bit of draft makes their bones and hooves more solid which can be very important when doing a lot of cross country and jumping.
TB Percheron cross (this is a 1/2 1/2 cross, a 3/4 1/4 cross would be lighter than this):
Selle Francais is also a very good jumping/eventing breed. If I personally wanted an eventing horse I would probably choose this breed.
My eventer is a clyde/tb cross. He maxes out around 3'7" though - could probably do a little higher but he's heavy-ish and really excels at the dressage part. He's a lovely mover and loves all of the eventing - actually stadium is his least favorite b/c he's less agile due to his size. But I adore him and we have a ball out xc or in the dressage ring!
If I could have any breed I would definitely get myself a dutch warmblood, they excell in dressage and are also fantastic at jumping. They are generally a sound breed unlike tb's (i love tb's to death though, but my boy is always going lame). A dutch would be my first pick :)