Okay. I know I've been quiet here, but that's because I've let an old favorite consume me again. Need somewhere to rant on this, it's numerical but not stat-topicable, so....
Space Empires IV random musings!
Earlygame: Only four techs with reasonable research rates and actual usability without high early investment (Stellar Harnessing, a 10k, requires a 50k first - Astrophysics) are Propulsion, Repair, Projectile Weapons, and Ship Construction. Of these, dropping Ship Construction after getting Medium Transports and Light Cruisers might be wise, as price gets prohibitive. At the beginning, you're looking at 2 turns for most techs, more if you aren't finding planets suitable for research. Thusly, once Projectile Weapons and Propulsion hit level 4, switching to research Astrophysics anyway (as well as species-dependent techs) is worthwhile.
Initial Build: Four ships are practical to build off the bat: Scout Ship (basics+6 eng+3 supply), Small Transport (this has two variants: either basics+5 eng+8 cargo (min)+3 supply (max) or 5 eng+11 cargo (max). I'll get back to this later.), Colony Ship (basics+module+5 eng+either Cargo or Supply, will also cover this later) and Base Space Yard (basics+Space Yard). Satellites and Weapons Platforms will be ignored for now.
Cargo Transport and Colony Ship: My general build is the 8 cargo/3 supply for transports, and Colony Ship with Cargo. Assume 25% reproduction in a year (I see minimum of ~33% because I focus on population.) This means a colony's population will grow 2.5% each turn. A colony ship with Supply takes 4 million population (only Cargo is the colony module at 20kt). A colony ship with Cargo (150 kt) takes 34 million (150 kt+20 kt.)
Home planets start with 8000 million people, or 8 billion. Average repopulation in a turn is thus 8000*0.025, or 200. You can thus have ~5 colony ships set out with Cargo and not upset the population's returning to 8 billion next turn. (6th isn't possible; 8000 number is based on population before they're taken), and the extra 1 turn of movement doesn't offset the really miserable starting population for a planet.
Now, Cargo Transports are trickier. 8/3 build takes 240 million people, and has 3 turns extra fuel thanks to supply. 11/0 takes 330 million people, has three turns less. Yes, this disrupts the population regrowth no matter what (and this is why I suggest not pop transporting to nearby planets if you aren't a pop. fiend). However, their trips are usually longer and, more importantly, repeated; they aren't oneshots like colony ships are.
Let's therefore assume that you're doing my standard build (5 base space yards, two colony ship producing planets) and also have a cargo ship moving pop from your main planet every three turns after the first). Base space yards produce Colony Ship every 5th turn, planets build Colony Ship every other. Also assuming that the entire pop crash hits on a designated turn A, and with the 8/3 design:
8000-(34*7)-240 = 7522. Pop regrowth this turn will be 188, setting you to 7710. Nothing gets build second turn, you're safe for another round. Pop regrowth kicks you up to 7903, two colony ships take 68 away and kick you to 7835, and that's within the range to get you to 8000 before the next cargo ship.
What if it's 330, though? Then your initial pop after the drain is 7432. First turn gets you to 7618, second gets you to 7808, which is just barely safe... except then you make the two colony ships, which hits you down below the 7805 threshold.
Obviously, these aren't the only build options; 9/2's not bad either, and it should just barely work out, right? ...actually it does, but only because you're not making any colony ships the turn after; you get to 7871, colony ships knock you down to 7803, your pop near-hits max but doesn't manage to, at 7998. Next turn colony ship steps in and takes 270, kicking you down to 7728, and the cycle continues, but it gets really close to slowly draining population.
Of course there are many other factors; you want a 10/1 at absolute worst, to me, as otherwise your range is pretty much 3 sectors which is no good. 8/3 gives four sectors which is far more useful. Once you have Stellar Harnessing you're not only doing far longer treks, but you're also likely carrying more (and hopefully, you have a Large or Huge planet - pops 12000 and 16000, respectively - fully populated to draw from instead). Still, 8/3 fitting worst-case scenarios and also providing max range for a small transport is useful.
Build Orders: Usually, Colony Ship (x2), Scout Ship, Colony Ship (x2), Cargo Transport, (Colony Ship, Base Space Yard) <-do while Base Space Yard count is 4 or less. Base Space Yards act as an extra, if slow, construction queue; equivalent of giving, say, Sephiroth a second action that goes at 0.2x average speed. Not useful immediately, but if you have five of them, all going at different times, the effect will definitely be noticeable. You can upgrade them later on to produce at 2/3rd Planetary Space Yard speed (as opposed to 2/5ths that rate), which helps immensely as well.
Species Techs: Temporal Tech sounds useful, isn't really. Organic's awesome for reducing reliance on minerals/radioactives, Crystalline lessens reliance on minerals. Religious is surprisingly awesome support, but its one ship part is immense fail. Psychic mainly just shares experience better, which isn't that useful.
Planet Colonization: depends on which game version you're using. Early on, Rock planets were easily the best due to resource/facility balance; however, after rebalance it shifted to Gas Giants, which just hold a facility number advantage (since resources kinda got rebalanced to not bork AI over). Ice is still worst as a starting option, but they tend to have the most ruins on casual observation. And free techs are good.