Multiple Research Strategy Questions

I usually go striaght for AP beams (Physics level 2) at the start because this stage is all about colonization and infrastructure so you aren't really building anything that you don't already have/need.

By the time you get AP beams your empire should have quite a few research points to spend on whatever the situation demands and you may have met some enemies so those beams will come in very handy. Also, Physics 2 gives you shields.

After AP beams I usually try and improve my ships first with things like engines and armour. After that it generally depends on the situation ie. maybe my enemy uses a lot of missles - it's off to PD research we go!

Never really bother with cutural advancements - they seem like a lot of research points for not a lot of gain.

I usually start with Sensors. A decent sensor level helps tremendously when scouting new systems, saving time and effort. Then onto engines. After I get the next kind of engine everything else comes - armor/shields/weapons/whatever. As for the cultural achievements ..I don't think I've ever researched them myself but I have gotten some from other aliens through treaties.

The only cultural studie I really like is math, ( or education in balance mod )
which gives a nice research bonus.

But not before I am a little farther in the game, they all give nice boni in the late game, so I give them 1-5 % when I can spare the points.

In the beginning I go for Research, Sensors, Engines, Shipsize ( until I can build flying shipyards to setup warp-point defenses ) and for PBM, PD and Armor, anything else, as I see fit.

Another early game goal is to get at least lvl 1 nature shrines and maybe time shrines.
Its easy to get system wide boosts which with other breather races surpases the whole planetary something tree ( i even can't remember how its called right now )

Remember : Pillage! then burn.
- Cpt. Kaff Tagon

I do not research "Research" until I've done colonizing. I'll trade, steal, and beg for the other 2 colony tech. Any technology that speed up your colonizing is much more efficient IMO at the beginning. If you grab a planet 2-3 turns faster, for every planet, will net more than just 10% research. Plus other side benefits (sensors is king, engines are good too). If you just get 1 extra star system without battle, how much is that worth? How many research stations can you put on that system?