I never managed to put my horse to training (at least yet), but I seriously considered it last year, so I checked number of local places (recommended to me). Here is the summary (and I'm talking about advancing VERY green horse):
Prices go from $600 to $1200/month including feed and training (MD/VA/PA area). I checked 4 facilities to compare and funny but $1200/month was the one with no stalls. I think it was way too overpriced (the trainer is nice though). Those for $600 were somewhat suspicious in sense of the horse care.
At least one place required to sign the contract and I think that MUST be done. That particular place charges $850/month, which include private(!) turnout and stall for the night and working with horse at least 5 days/week. They are EXTREMELY serious about keeping horse safe, so they said they won't even put both my horses together in same paddock to avoid possible injury.
Actually I seriously considered the place and the only reason I didn't go was my paint freaks out with strangers and I mean FREAKS OUT, so she could clear the fence (which she did before and I've witnessed that at least once) and just run away.
First, you have to state which shots the horse must have and (of course) current coggins.
Second, what is your responsibility if the horse gets injured
Third, what you'll do in case of emergency (say, colics, lameness, and so on).
Personally, if the trainer got injury while working with the horse that's trainer's problem (of course considering the owner did not try to hide the fact that his horse is fire-breathing dragon and try to kill people and honestly told all possible troubles with the horse). That's part of the job (sorry if it sounds harsh).
Also, giving even small discount for multiple horses (say, $25 off the horse) sounds extremely attractive to the customers.
In any case, good luck in your new start!