Don't rush into a decision just because you are promised a discount if you sign an agreement now. Be sure you understand what work is to be done for what amount of money. It is not generally a good idea to pay in full until the work is completed. Most reputable tree care companies have all the work they can handle without going door to door. People who aren't competent arborists may solicit tree work after storms, seeing an opportunity to earn quick money.
Storm damage creates high risk situations for both workers and property.
If possible, get more than one estimate. A conscientious arborist will not use climbing spikes except when removing a tree. Climbing spikes open unnecessary wounds that could lead to decay. Good tree work is not inexpensive. A good arborist must carry several kinds of insurance as well as pay for expensive and specialized equipment.