Bruce, it's early sunday morning here, I wouldn't expect too many answers if I were you just yet.
As for gearboxes, it's not a matter of LR offering different gearboxes; the lt77 is an older gearbox and the r380 is a later gearbox. Which is the most suitable for the task you have in mind depends on the engine that you are going to use and the practicalities of fitting that gearbox to the engine.
I have an lt 77 on the back of my 300 tdi for no other reason than it was there when I bought it, it has 5 gears and a reverse and was exchanged for an exchange from Ashcrofts a couple of years ago. I can't see what difference fitting an r380 would make to mine !
If you want a stronger gearbox then go for the 4 speed lt95 from an old manual Rangy or the later Lt85 5 speed santana box. If you want to be exotic and gain lots of kudos then fit an auto.
HTH
Mo