I can tell you who NOT to use: Equine Logistics. They were hired to pick up a horse from one of our clients and deliver him to the South. Gave the seller a very hard time, didn't show up for almost a week and in the middle of the night at that.
Couldn't get the company on the phone. Couldn't get a straight answer about when they were coming, was supposed to pick up on a Saturday, didn't get picked up til Thursday and wasn't delivered until the following Tuesday, if I remember right.
When buyer asked for deposit back, they refused despite that they were not even remotely close to the scheduled pick up date.
Once when seller called driver to find out when he'd be there he said sometime between 11pm and 6am 2 days later. so she said so what am I supposed to do- keep him wrapped until for the next 2 days? Driver said I don't care what you do. Not my problem and hung up on her.
Don't use them.