Research for Dummies?

The philosophy techs - which give +50% and then +100% to research points - are an absolute must and should be researched as soon as they become available.

The education techs are more situational. As Prussia>NGF>Germany I didn't research any past the first level as you start off fairly literate and can just encourage clergy and keep education spending high. If you start off with <20% literacy I'd say they were a must have, at least up until Biologism.

In the early game your plurality is low, so Ideological Thought (which has something like +50% plurarlity boosts) is extremely useful.

Use NFs to encourage clergy to the magic 2%, then consider shifting encouragement to clerks, provided you have the industrial base to support them.

In terms of essential techs:

• Army - Tactics, light armaments and doctrine are all good branches, although the other two are nice to have as well. You can ignore artillery and cavalry if you need to though.
• Naval - Naval Construction and Naval Engineering will give the biggest improvements to your ships. Doctrine will also give combat boosts, but to a lesser degree.
• Culture - See above, Philosophy is by far and away the most important branch.
• Commerce - The banking line is good for Business Banks, which unlocks the 'Commercial Retailers' event, shrinking farm sizes by 20%. Good if you need the POPs for craftsmen. If you're nowhere near filling your RGOs then it's of limited use.
• Industry - If you're planning on heavily industrialising then many of these techs are good. Medicine gives a nice population boost, a chance of a great prestige boost and lowers attrition. Railways will make your factories more efficient, as will Energy and Mechanisation techs. Combustion Engine will give the 'First tractor in ...' event, which will further shrink farm sizes. The metallurgy line is good if you have a lot of coal/iron, but can be ignored if not.

Pretty much seconding what Dewirix says. Check out the "Killer techs" thread for which ones you want to prioritise.

If you have good literacy (i.e: 60-70%+), focus on the +RP techs and the early NF techs for Plurality boosts, then go for other decent suggested techs, putting your NF's to work for Industrialisation. If you have poor literacy, make sure you get Bioligism and encourage Clergy like mad. You really want to prioritise raising it now so it pays off longterm. Also, if you don't have it, research Freedom of Trade on Day 1 (many Latin American nations don't start with it, as far as I know all Uncivs start without it).

To add to what Dewirix said about everything else:

• Army: Tactics is always useful. The Arnaments line is brilliant (note Machine guns is a life rating tech). Fort line is decent, but Tanks require a high level tech here. The others however only get good near the end, with the Cavalry tree allowing Gas Attacks and Aeroplanes (and the first level techs, if you're playing as a nation that doesn't start with them). Artillery as a line can probably be ignored, however the final tech there gives decent tank boosts. Otherwise, everything here is useful.
• Naval: Personally I find the Naval side lacking in depth compared to the combat side. I only prioritise getting the Ship unlocking techs up to Dreadnoughts here. The only other thing worth noting is you may need higher Naval bases depending on where you want to colonise. If you plan ahead though, you can ignore this. So if you wanted to go on colonising Africa, a land grab in the Middle East or Eygpt would allow you to colonise Somalia (and from there on, anywhere with a land link) with only Level 1 Naval Bases.
• Culture: RP techs are a must have. As for Education efficiency, Biologism gives Darwinism, providing a massive EE boost. Early NF techs let you boost your plurality and Nationalism/Imperialism is one of the Life Rating techs, otherwise pick them up when you can access the NF point it unlocks. The Reinforcement/Experience tree is a bit of an unknown to me, but the last tech there gives inventions unlocking Radios and a +25% EE tech, which are useful. The +Prestige techs are generally lackluster. If you need for some reason to become a GP quickly (e.g. You're Sweden and want to form Scandinavia ASAP) the Prestige can bump you up there, but otherwise it's poor. However, you may find the +RP techs and/or Medicine can do this for you.
• Commerce: Most techs here are inferior to the Industry techs. Freedom of Trade is fantastic, and Business Banks give a nice event. Most of the rest I save till late game once i've gotten the decent Industry ones out the way, or just using the Lower Level ones as filler techs because they're cheap enough.
• Industry: Medicine (Life Rating invention), Electricity and Combustion Engine are fantastic techs. Getting all of those also gives you a bunch of nice goods that it takes a while for other nations to grab (Automobiles, Planes, Fuel, Electric Gear, Telephone, technically Dyes aswell though they make poor factories). Mechanisation techs are notable for inventions allowing Machine Parts and for another nescessary for the Canal decisions. Railways are always good, especially as they increase RGO output aswell as Factory output. Clean Coal is a must if you have any coal producing province. Only go further down if you actually have ample Iron or other resources to make them worthwhile.