Over the years Tuckers have had various engines. I know they used the 318 Industrial as well as the 360 Industrial and also the 440 Industrial, depending on year, model and options. They've used various Diesel engines such as the 4-53 Detroit, some Perkins Diesels and ones from Cummins, too. They also used an Industrial Hemi "back in the day"....
The tracks look "rusty". One thing I'd be very concerned about is the condition of the flanged track bearings. Each grouser bar has two and there are something like 30 grouser bars per pontoon and four pontoons. So quick math is 240 bearings.
They aren't available from Tucker anymore and IIRC Cook's Equipment in Vermont had some reproduction ones that were in the vicinity of 40-50 bucks each. They probably all wouldn't be bad, but it could get really expensive... really fast.
As far as loading and unloading I'd think you would be fine winching it onto and off a trailer. I have kind of a Rube Goldberg trailer setup. It's just a 10,000 GVW car hauler with some RR tie cribbing on the deck to get the tracks above the fenders. It's not real pretty, but it works fairly well and I've probably put close to 4,000 miles on the trailer loaded with Tuckers.
Hugh, I understand your passion, and your desire to get one to start working on. Honestly though, I think you'd be better off finding one in better shape to begin with.
They do show up from time to time. For example about two or three years ago there was a pretty nice 543 on KSL.com. It was fully operable. That machine had the sedan style cab and the wider pontoons (both desirable features, IMHO).
I kind-of lusted after it but I was hoping Weatherby would get it and I didn't want to buy it out from under him.
Good Luck!