make absolutely sure that the tree service is licensed and INSURED.... because if they make more damage - too bad if they aren't.
I'm wondering about the one that "doesn't write out estimates" - that means he can present a bill for any amount - "What estimate?, I never said I'd do it for $600".... see how that works. Don't even present that one to the insurance.
The second one sounds like the most likely but do make sure of the insurance/bonded/ or whatever
our daughter and former SIL had their own tree service, our grandson and his half-brother have a service, my best friend's husband has a tree service....
get everything in writing, AND make sure they are insured..
did I mention to make sure the company is insured?