I personally like how it was handled in Alpha Centauri. First and foremost, if you want to choose blind technology, you can (in the options) before starting a game. From there, every so often when you make a tech breakthrough you get a window, asking you what your scientists should focus on next (conquering, exploring, discovery, etc.)
From there, techs would increase in tiers, and you would decide the generalized direction and what would come of it. For example, researching into conquering technologies would yield new weapon options to study about, while at the same time new techs in other dominions are open. And learning one thing may lead to another...you may learn enough in Conquering to gain access to ships. You need the knowledge of ships to go out and built stuff in the water and on the shore.
OR...let certain things happen because of techs. For example, I'm researching Production, and I get the knowledge to build a blacksmith. I'm so excited, I build said smithy, and some guys go to work there. I then turn my attention to, say, farming. As I'm studying farming, the smith knocks on my door, says, "Hey, boss! I've been playing around with stuff in my spare time, and I learned how to make a sword!". From there, the Swords tech is available, with the first one given.
Building a farm would give me a chance to increase knowledge on farming, and that randomness would occur based on farming. Perhaps I begin with bone tools. Then, one day, a farmer, a carpenter, and a blacksmith go into a tavern and come out with an idea for a hoe. They come to me, say "Hey! We combined our talents, and we made this fancy tool for farming!"
That way, randomness could happen just be building enough in areas. If I have 20 farms build, 10 smithies, and 10 carpentries (is that a real word?), then I have 20 farmers, 10 smiths, and 10 carpenters. They're all going to think about what they want, and maybe they'll get together and work it out. But, if I'm not willing to wait for them to figure it out, I just go to my researchers and tell them to start working on farming stuff, and get the hoe technology that way.
In such a manner, you would accumulate a greater chance at random happenings for each building you have aligned with an area. Armories and barracks may think up new weapons for soldiers, just as a smith might. You can research them normally along a tech tree, but I don't like the idea of having X number of farms, or smiths, or whatever and not have them think up something new once in a while.