Adam:
Thanks for posting the link to the pictures. That appears to be a kit barn from a company in CT. I have seen that type before. You'll find that a lot of the nailers between timbers are secured from the outside so that the nails don't show on the inside.
The main frame is timber framed but the roof and siding are usually standard stick built construction.
You should start with a complete set of drawings showing where everything is.
You'll need a floor plan(s), elevation views and bent drawings.
And then label the drawings and the frame with the same labeling system, before you take anything down or out. One system we used before, at a guild project, was to take round metal discs and secure them to the timbers with screws. Each disc was stamped with a numbering code number letter combination. This prevents the markings from fading or being washed off in the rain. And the labels last. Lots of parts are the same, and may not need labeling, but the main pieces should be labeled.
Once it is all labeled then you can start removing things. Striping the roof and taking off the roof boards pretty near last to save on water damage as you do the disassembly.
After the siding is off and the roofing is stripped, and the roof boards are off you'll have just the frame. Taking down the rafters and taking out the nailers shouldn't be too hard. You probably won't need a crane for that.
Once the nailers are out then the bents would be lowered (you may need a crane for that) and as mentioned pounding out the pegs to take the tenons out of the mortises. Most of those braces appear to be nailed in, so they should come down with the bents and then removed after the bents are horizontal.
I built an addition onto a barn very similar to the one you're showing. And the owner has the name of the company in CT where he got his kit from. If you'd like me to ask him the name again, so you can look up how much a new one would cost, I can do that for you. Send me a private email and we can discuss it.
Jim Rogers