Be certian that he has full insurance coverage-- for any damages he may cause to your or neighbors' property AND damages he may cause to himself. As with any contractor, get his insurance firm's contact and obtain verification of his liability and workmans comp in writing !
$1300 to fell that many trees is a fairly low price
As far as keeping the wood to burn-- nope-- Dont burn pine in a fireplace/stove. If it were me, I 'd go ahead and have him haul off the wood and debris. It may cost you more $$ and trouble to get rid of it later.
If they're large enough trees and are in good shape, you may be able to find a timber/lumber firm that will come haul them off for free.