Good arborists generally offer a full range of services such as pruning, fertilizing and pest control. A good arborist will seldom ever recommend topping a tree and only then after severe physical damage to the tree's crown. Branches should be carefully selected for removal. A conscientious arborist will not use climbing spikes on living trees. Be sure to have a contract.
Most companies have their own forms.
If the tree is to be sprayed, get a written statement detailing the specific insect or disease to be treated and the chemical to be used. If fertilizing is to be done, it should be stated how much fertilizer will be applied by what method. Specify what cleanup work will be done and when. Determine who gets the firewood and if it is you, determine where the wood will be stacked and the size of the logs. Clarify if removal of the tree includes grinding out the stump and even filling with soil and planting grass.