For what it's worth, I'll post my experiences with cranes. I rent cranes for about $120 an hour, 4 hour minimum. The operators they send out with the cranes have experience with tree removal. This is important; they tell me that doing tree work with cranes is much more difficult than any other kind of crane work. I can imagine why: you don't know the weight in advance, and you need to estimate how the material will move after being cut.
This is how we proceed: Once the operator arrives, we discuss the removal and work out a rough plan. He positions the crane wherever he thinks it's best (with my approval) and sets up the outriggers and extends the crane. I hook into the ball and ride up to the place on the tree where the first sling will be placed. I sling the branch onto the ball clip with a girth hitch, then lower myself down to the site of the first cut. The crane operator tells me where he wants the cut by signaling to either keep going down or stop and "cut right there." He applies tension with the crane so that the piece does not fall when it's cut. I make the cut as high as possible, just in case. This is tricky, because this means that the saw is shooting the chips right into my face. Safety glasses are critical, otherwise you get chips in your eyes and end up trying to get them out while the crane operator and your ground guys wait around. Once the cut is made, sometimes the crane operator needs to lift it a little more. It usually comes off in a very easy and controlled way, without much movement. The operator lifts it and drops it wherever we decided the brush would go. During this time I may or may not be repositioning myself, depending on how difficult that is to do. I often stay put so I can put the sling near my last cut. I also might stay there because the crane can get me to my next position much more easily than I can spike there. He brings the sling back, and we repeat till it's done. That's about it.
If you only have access to crane operators with no tree removal experience, I would reccomend putting them on a removal that is low-risk and easy to do. My first crane removal could have been done easily with ropes, but for my own sake I brought the crane in so that when I did really need a crane, I would be ready. Perhaps if one of the operators you know can get his feet wet on an easy removal where a mistake wouldn't be a disaster, he could approach a trickier removal with confidence. Or maybe not. Only you know if that would really work or not.
To answer your hardware question:
When I hire a crane, it's usually the largest size, which can lift many tons. We usually stay far on the safe side because of the dynamic nature of tree removal. We usually take out pieces under a ton, which can be quite large still. I have taken out 30 foot sections of spruce with a crane that were still under 1000 pounds. They provide the slings, which are rated for 20,000 pounds. I always use a girth hitch to attach the sling, since it's easy to do and the strongest possible method of attachment. I use my little Husky climbing saw to do most of the cutting, and use my regular harness, climbing line, lanyard, and spikes. Once you've done one, you'll see it's pretty simple for the climber. But that operator has got to know what he's doing! My two cents.