It’s been a while since I played (and that was a few versions ago) so some of this might be slightly off.
For how the computer researched stuff so fast you have to understand how the economy works and it’s kind of complicated.
You can adjust your tax rate panels (empire management? I don’t remember for sure). You wanna jack the taxes up as high as you can and still maintain ~50% popularity. There a breakpoints at 50%, 60%, and probably others where it drops alot more then normal, so you will probably want to put it at 49% to start out till you can get more happiness buildings going. If you’re on a lower difficulty or you picked morale traits you can probably go higher from the start. There are penalties for having too low morale, though I don’t remember what they are offhand so don’t let it dip too low.
Spending rate (probably not called that) is right below that, you want to bump that up as high as you can and still have a positive income. If you get lucky finding money from the goodie huts you might want to bump it up to 100% for a while to spend the excess.
Below that are sliders for social, military, and research spending. These work with the above slider to determine the percent of your factories and labs that are being used. Unlike most of these types of games, factories and labs don’t actually produce anything - they just convert money into either hammers (social and military production) or beakers (research production). Putting the spending slider to 100% and the research slider to 100% means 100% of your labs are being used at full capacity to turn money into beakers. Running 100% spending and 50% research 50% military means your labs are running at half capacity and so are your factories when they are used to produce ships.
Unfortunately, you can’t run everything at 100% (even if you can afford it.) so you have to pick and choose. You probably want to bump military (shipbuilding) production up and maybe social (planetary construction) to start out with to get those colony ships out quicker. Once you’ve colonized everything you can, you can turn military down (or off) to get buildings and research done faster.
Note that excess social production from factories gets turned into military production (maybe the other way around), and excess military production gets turned back into money so there is no loss from that.
A general good start is to send your flagship around looking for goodie huts (which are space debris in this game). It starts with a survey module built in, which lets it open them and the rewards are generally very good - try and get as many as you can before the enemies do! Build colony ships and send them to every star in range - if you have a certain tech (stellar cartography I think… some races start with it) you can see which stars have planets - no use sending a colony ship to stars with no planets. You can build scout ships, but it’s usually best to just scout with the colony ships.
I usually build a factory on every new world (the colony base does not really produce enough hammers) then I specialize them. Small worlds with few slots get a few food and tax buildings to make some money, larger worlds get a bunch of factories to build ships, and so on. I’m not sure if this is the optimal strategy but it helps me keep track of everything, anyway.
As far as research tips, this advice might be out-dated because like I said I have not played for a while but weapons are generally much better then defense as far as cost effectiveness (guns are good vs two armor types and weak vs one, while defense is the opposite - good vs one, weak vs two). Pick a weapon type, there are slight differences (lasers, for example, do less damage but are smaller so you can stuff more on a ship) but it does not really matter.
Research the best (smallest) of the first ‘tech’ of defenses, and put a single one of each on every ship - the wrong defense type counts half it’s value anyway, so for example shields count for 50% against mass drivers. It’s rounded up though, so one of each type gives you 3 points of defense vs everything for minimal space cost which can be helpful early game.
Starbases are incredibly good, don’t neglect them! galactic resources (the little floating colored shapes in space) can make a HUGE difference so capture them whenever you can and upgrade the starbase they are on (fly another constructor into the starbase). Try and destroy the enemy resource starbases too - he won’t usually build guns on them so you can make a few small fast ships to zoom around blowing them up. You can also build trade, economy, military, and influence starbases anywhere - economy ones are very useful near your planets and military ones can buff up nearby ships ALOT. I’ve never had much use for trade or influence ones personally (but then I tend to shoot first and ask questions never).
…this is running kind of long, sorry about that. Hopefully it helps though, and feel free to ask if you have any other questions.