In addition, note that the AIs don't research all those technologies themselves: they do a lot of technology trading between one another, and you should do the same!
Trade basic technologies to all AIs in return for technologies that are useful to you; if you have some available cash, you may want to buy the technology from them, rather than giving them some tech in return. Note that you shouldn't pay too much when trading: the AI will be extremely unwilling giving up some technologies (mining, weapons) so you should research those yourself rather than paying through the nose...
Does this help? Feel free to post back if you're still having trouble!