I've found that if you keep your mid range goals in mind, the exact order you take the techs isn't that important. If say you plan to start your conquering when you get some decent medium hull ships, it doesn't matter too much in what order you researched engines, weapons, defenses, miniturization, etc. The same goes for happy, productive planets -- if you realize you will need upgraded factories, markets, farms and research, the specific order isn't too crucial and is usually pretty obvious anyway depending on where your empire is currently falling short.
One key I figured out is not to research too many consecutive planetary upgrades. If most of your planets already have, say, three or four factories and labs upgrading, that's not the time to research upgraded markets, for example. In practice, this means going between ship and combat oriented techs and planet upgrade techs depending on if my planets' build queues have room for more stuff.
Also, cheaper is better. Even if that tech that takes 10 turns to research would be more helpful than that one that would take only two turns, remember that you can also probably research two or three more techs in those ten turns that would cumulatively be more helpful, after which that 10 turn tech might only take 8 or so turns because of intervening research improvements. This means, for me, that I tend to spread the research out a lot to the various branches and not jump up ahead too far on one branch, with a few exceptions like hull size and minaturization where i really want to get a jump on the competition. I will also get ahead on whatever techs suit my particular goals that game, such as trade, or diplomacy, or soldiering, but even there I try not to get too far ahead in any particular area.
I find the whole process pretty intuitive and stress free. As long as you keep your medium term goals in mind, you don't have to stress too much about the exact order as long as you don't fall too far behind on a crucial branch or have a particularly pressing short term need. For which I am thankful, that is a bear of a tech tree and I'd go nuts if getting things in a particular order was more important!