Get a few bids. I have found that tree removal is all over the board. I am a pool/landscaping designer and have to get quotes time to time for remodel projects. I always have a client deal direct as it can be a little rough.
I have had one guy bid $5K, the next $10K and the third $15K on the same project. The $5K guy pulled out an electrical wire that was wrapped in the roots of the tree. That wasn't a surprise as he can't see underground. What did suck is he just stopped responding to calls from the homeowner. Had he just firmly state that he isn't responsible, and he isn't, the issue would have gone away. I believe I quoted $750 to replace the run when doing the installation. So the homeowner still saved $4250 over the next bid.
On another tree trimming job, the quotes were $600, $1200, and $2000. The $600 was incredible hard to communicate with, so the $1200 bid got it. He will get their return business in the next year or two when the tree needs to be trimmed again.
Try to get a payment schedule of half up front and half on the back end. That way you have some recourse if there is an issue.