Where to go on the tech tree??

Start with Xeno Research. The improved research facilities will give you a good head start.

After that, I usually go for the (relatively) cheap planet and research improvement techs. Once I've got the economy and research humming nicely, I can research any weapon/armor/invasion techs I need, pretty quickly.

Even better, though, is when I can trade a high-level weapon/armor tech with another civ. That way, I get a big jump in research (I don't have to spend time researching all the early weapon/armor techs), and since I've been focusing on building up my research and planets, I can usually end up leapfrogging past the civ who gave me the weapon techs in the first place.

That's just one tactic that seems viable, though, I'm sure there are many others

Yeah, I've usually had quite a bit of time to get rolling in games, so there hasn't been an immediate rush for anything other than colony ships. Anyways, first thing I go for is Stellar Cartography, meanwhile I get some colony ships together, and once I see some promising-looking systems I'll send them off in the relevant directions. If the map is larger I'll usually head for a life support tech or two, so I can get ships further out sooner. Then I switch and start building my colonies up properly, and I go for various base-level factory, research, and farm techs. I'll pick up diplo stuff on the way, unless I have a dire need of something else, and then I'll move on to some early weapons and defenses.

Also, it's usually a good idea to go for Xeno Ethics pretty soon. I can't remember what Good does, and I've never chosen Evil, but Neutral removes the need for building, or even researching, anything like Soil Enhancement and the like (Among other things.). It can be a very nice boost when every planet in your empire gets one to four new spaces to build on with no investment required.

Then build a small navy with the early techs, and from there on out what I go for depends on which kind of victory I'm after.

I'm sure there are plenty of other viable courses to take, though! So experiment and play around until you find something that works for you.

I go Xeno Research first off (start with Cartography and the first three Propulsion techs). After that I poke after a few "quick" researches...usually opening up with the improvement tree that lets you upgrade banks, factories, and the like. Then I'll go long haul and research the entire Sensor tree so that I can build the Eyes of the Universe and then it's to Ethics for me as well. Neutrality for the same reason as above. If I can get there before I'm done colonizing, the purchse bonus can help in beating out other races to distant planets. Starports are only ~150, and then you can purchse a ship here and there close to the "frontier". After that it's a smattering of things here and there working towards faster ships (last tech before Warp drives IIRC) and the nice 8pt mass drivers while building up my infrastructure and logistics. A few influence improvements are important as well so that you can toss up some effective starbases to flip planets.

Blif

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!

I tend to go for universal translators first, followed by drives until I get the first general speed increase, after that I go for increased research and manufacturing for some time. Little point in getting way ahead of what your planets can realistically build, but researching industry also helps with mining star base modules. After that 1 influence tech, then sensors,shields/weapons. It's good if you can get the Translator and the Hull Plating wonder early i.m.o.

B.t.w. constructors, I find, are a lot more accessible than in GalCiv 1. I've found myself building 2-5 colony ships and then 2-3 constructors in quick succession because I've located resources by then ... the price difference is much reduced from what it used to be.
I find I can also be a lot more careless w.r.t. how many colonists I put on the new planets.