Most definitely have the harder stuff go out first! Don't sell the cream and be left with the skim milk.
I've had people like this. I agree to take all the wood if I'm in need. I've had people want me to take all the brush too, even in towns where the town picks up brush. I've offered to drag it to the curb for them but they didn't want that. Passed on that one.
That's how I do it. You promise to stop taking replies and let me get all of it, and I take the ugly stuff first and buck the rest to length so if I flake you will get rid of it easily. Same goes with multiple species. I take the less desirable first in return for the privilege of having first dibs on all of it.