Green oak construction is an interest of mine although I only have experience via courses and some limited work at a framing yard so I won't pretend to be an expert.
I've worked with oak and douglas fir and while the oak was a dream to work with, the douglas fir is a bit less over the top for a conservatory (does one need a conservatory to last 300+ years?).
I don't know what the price difference in green oak and green DF is but the latter must be cheaper. Cost was a major reason for its use in the project I worked on.
Don't worry too much about oak tannin and tools, just a wipe will do but use a barrier cream on your hands as tannin can cause sensitivity in some people.
The checking and moving should matter less in a conservatory as its not well heated, anyway if you don't like checking and cracking you shouldn't be going down this route… just build a Victorian conservatory instead (the plants will like the extra light too!)
Yes green oak is v.heavy! You need an extra person on hand when moving or turning the posts, a heavy duty trolley helps for moving stuff and heavy duty trestles as well. You may need several people around for the raising or a "roustabout" (telescopic lift) or a ginpole or if its really huge, a telehandler or crane.
I think the Jack Sobon book uses the square-rule setting-out technique used in N America on straight softwood, not windy european oak. This harder to pick-up than mill-rule/ scribe rule traditionally used here.
http://www.wealddown.co.uk/Courses/courses-building-conservation.htm#bc timber scratch do very good courses in this type of building and lots of info can be picked up. You build a 10' square single bay. Not a cheap course though.
A guy called Henry Russell does one or two courses each year and packs in a lot of info. He's very good and you should be able to find him via
http://www.carpentersfellowship.co.uk/
Finally if you fancy someone along for the ride PM me as I love any excuse to get out my framing chisels!