Welcome!
The '83, eh? If I remember correctly, that year was the twin's last year, and was only available outside the 'States.
There's alot to tell about the twins, but I'll just start by responding to a coule of the things you mentioned:
The "LTD" moniker on the side was actually the line name for all the 750 twins from '76- '83, though the letters were only stuck on the side of that latter. The "LTD" style came to be known as a bit more laid-back, stepped seat, etc.
The electric start on the old big twin is famous for failing - does yours have a kick start, too (I hope)? Just search for "starter clutch" in here or the old version of the form, found at the "archive" link in the menu/toolbar above.
Taken? Nah. I paid $600 and $400 for mine, so I figger we even out. You got a good deal if it's nice, and a less than that if it's less than that.
There are a few 750 Twin owners here, and we're glad to help when we can. In fact, most everyone here is helpful.
As for info (like a manual) good luck. Because your model is more rare, it might be tough. Some guys get the manual for the older bikes like mine, and just deal with the differences. The engine is almost the same after all....
Enjoy!