Best Research Path

yeah, mostly you need to focus. At the same time, you're right. Go after what you need It is a good idea to plan ahead sometimes though. I usually don't start on any research between 1865-1870, because then the techs that come in 1870 will get done superfast, usually. (because tech points get saved, thank god!)
That way I can, say, colonize Africa (because of Machine Gun) a few years before the rest, because they start on the tech in 1870 or later, while mine starts in 1870 but get's done within days. Of course that depends on how the tech before ends (if it ends in '64, I might start another tech that ends in '67, thus I only save points for 3 years..)

Tech points get saved?!
Why did I miss that? That's huge!

Yeah, people do this thing with saving up RPs, but it only would make sense to do when you're one level away from the techs that are going to get researched and when all the other techs would give too marginal of a benefit to be researched now. Keep in mind that you are also missing out on any benefits to other that you could have finished during the time that you're "saving up" (tech improving Industry, Prestige, RP accumulation, etc), so it's not always a perfect strategy.

http://forum.paradoxplaza.com/forum/showthread.php?492256-Killer-Techs&p=11503618 that thread has a lot of advice on tech choices. You can find it from the FAQ forum

For civilized (assuming most tree's start with 5/30), I usually follow the following:
Ideological thought (for those pluralities, will speed up getting the other tech very well)
Medicine (I'm not very democratic, so social benefits take a while this will patch lack people well, and attrition is the big killer of armies anyways, so higher supply limit wins over most army tech too...) OR, if it's already 1840, this comes third after
Idealism (for the 50% research and some prestige)
After the research is taken care of, I usually go to get those industrial ones,
Mechanical Production and Clean Coal on top.
Alternatively if military situation looks desperate,
Light armaments and Army Leadership
...
I ignore commerce tech, probably too much really, but just go with the 'research speed first' then the other needs, and you can get along quite well...

I'd say for tech strategy, make sure to always research the research boosting ones as soon as possible; count how much RP you'll need and save up that much so that you can get them at the instant they become available. This'll maximize the time you can research at top speed, and give you a very high chance of netting 100's of prestige points thanks to being at least a year ahead of anyone else at researching them. Plurality-increasing ones, especially Ideological Thought and State & Government are good for boosting research speed too, though they affect other parts of your society in ways you don't already want. Apart from that, it depends on what your nation needs. Medicine increases your pop growth which means that the earlier you get it, the bigger the benefit in terms of population. Also, Freedom of Trade should usually be your first tech if playing a nation which doesn't start with it. In that case, I usually start with FoT, then save RP until 1840 and instantly research Idealism.

EDIT: On general strategy, apart from that, it depends on how you play. If you plan to fight a lot of wars, you should really prioritize military techs since they make a huge difference, especially early tactics techs and the attack/defense ones (the two to the left). If you plan to emphasize economy though, I'd spread research more evenly in, get as many techs as possible since there's no real killer ones in the same way as with military tech, you'll get more of an edge (generally) from having many industrial and commercial techs research instead of spiking ahead in one field. Culture on the other hand is more like military, you'll want to get specific techs (the ones with prestige point inventions) ahead of everyone else to really reap the benefits, so prestige strategy means specializing in culture tech. If you have a cultural or military strategy, it usually makes sense to pick the research school that benefits it.

For unciv, education efficiency, extra NF and extra RP tech is the most important tech. Even more important than industrial tech. I usually prefer to get all philosophical and education efficiency tech before taking any industrial tech. Military tech and naval tech are not that important too, when your civilised, if you can get some protection form a GP.