I agree. However, I think the main thing that must be remembered in making a tech tree is much of the research time/cost needs to be less off discovering the technology than reconstructing what is needed. For example, at the beginning of the game, there would be enough people alive to help teach people the basics, say of medicine, the need for hygiene, germ theory and the like. However, to get to the point of of invasive surgery, you'd need to have mastered chemistry again to, cultivated some sort of opiate or be able to make/use ether, not to mention have the facilities that will have the lights, is clean and the like.
I have often touted S.M. Stirlings "Island in the Sea of Eternity" books and I'd also seriously recommend the whole Eric Flint (et al) series 1632. especially the associated "Grantville Gazette" which is available in book and online at
http://www.grantvillegazette.com/. Both stories are about a future city thrown back in time, the first to around 1200 BC the other to (obviously) 1632. All these stories deal with up-timers having to make do with less. A lot of these stories show that BIG problem is that often times people know how to do certain things, but they often lack critical elements or more often chemicals that today are easily mass produced. So a lot of the initial problem is assessing what they have, what they can salvage (1632 shows how important machined bolts and screws are and how long it takes to make them by hand) and then what will the need to go forward from there.
Plus, I'm sure there would be a lot of times at the beginning of the game, 20 years after the event, the group might have the tools and the resources, but might lack some critical bit of knowledge. Sort of like knowing how to build a car, but no one knows how to create ball-bearings. That's where I believe that the goody huts shouldn't just gift you with a technology, but represent some person with knowledge, some critical book or some tool that could be copied so that a good hut would give you a bonus toward a technology. It would be nice if there could be a way for it not have to be the tech your researching but that's probably not possible.
So I'm thinking that many of the first techs would represent a lot of these cottage industries that make many of our basic techs work. As mentioned above, Chemistry would probably be one of the first critical techs prior to a lot of other techs like medicine or gas extraction and the like.
Again, I recommend these books. Best of all, in the Grantville Gazette, they have these works at the end of the book where people discuss the feasibility of certain projects. I'm getting ready to read "Drillers in Doublets" which is all about different power sources from coal, oil, water and the like.