Welcome Cancotree
First thing you'll never have enough !
I don't know much about what you would need for tree work specifically but for general work here's some of the items I have that are used regularly.
4 - 6 ft. Wire rope chokers
4 - 16 ft. Two inch double web slings
2- 10 ft one inch web slings
1-four part line bridle. Mine is 3/8" x 16 ft. Longer maybe 20 ft. Would be better
2- tag lines. I have two so I can rotate them, a dry one and a wet frozen one
At some point you will wish you had a pair of spreader bars mine are adjustable to 10 ft.
Oh! And you will need a bunch of shackles, for a boom truck the weight rating isn't as important as the opening so you can fit them over stuff ,I find 7/8" are very useful.
The list goes on and on but the above will let you do a lot of jobs without jerry rigging stuff ( safer and more professional)
Good luck