Hi - I'm so jealous I can barely contain myself
Well, depending on the set-up, I normally pick whatever tech is most costly as the freebie after liberalism, but if I am already falling behind in military strength, I might go for something that helps me there.
I mainly go for CE, but I diligently try to go for some city specialization as well. My most succesful (i.e., least disastrous) attempts have all been with Elizabeth as a leader, so I try to have a science speciality city built up with a science academy and at least one super-scientist and a more production-oriented one to get some nice engineers. All that, and I try to develop economy as well.
Having played all the previous civilization games, I have developed a pretty defensive atitude: I generally do not like to attack before I have armor... could that be a key to explaining my failure? Also, I have speculated that I might go for advanced civics etc. too soon...
oh - for techs researched after liberalism, I usually go for a mix of older techs I have missed out on because of bee-lining for liberalism, and techs leading towards consolidating my economy...