I love my Morgan like everyone else said they have very level heads and mine has never spooked and couldn't care less about all the things I've thrown at him (he just tries to eat it). Also, he is a very easy keeper even at 18 and most people think he is much younger than he is. The thing about Morgans is that they're a very varied breed. There are a lot of Morgans that are probably mostly saddle bred and so they will not be the same as a foundation ("pure-er" bloodlines and closer to Justin Morgan). However, I have never really met one so I can really comment on their conformation. My Morgan is foundation but is a "Government Morgan" so he was out crossed to thoroughbreds and looks a lot different than a "Lippit Morgan" which will be the most "classic". As far as disciplines go I would look at his pedigree and see which family he's from and if you can find what his parents did.
P.S. Morgans originated from one sire, Figure, later called Justin Morgan after one of his owners. As far as I've read there is no proof who is sire and dam are so no one can say from what breed Morgan's are descended from. However, on the online pedigree data base it says he descends from a thoroughbred and an Angloarab. I don't know how much evidence supports that but I personally can't see a Morgan coming out of that mix but that's my fairly uninformed opinion.
Sorry for so long a post I could talk all day about Morgan history! Lol hope the info helps and good luck with the horse search!