If you don't mind abusing the target prioritization algorithm a bit: when you design your warships, design a ship with almost only defenses and the drive/life support components you need for your speed and range targets, and set that ship's role to 'escort' when you save the design. Then design a ship with almost only weapons and the drive/life support components you need for your speed and range targets, and set that ship's role to 'capital' when you save the design. Build an escort or two and a pile of the capitals for your fleet, and watch the glass cannon capital-role ships murder things while the computer's fleets waste time trying to burn through the defenses of the more or less harmless escort-role ships. Toss in a few support-role ships carrying fleetwide bonus modules to further enhance fleet performance.
You may (or may not) have noticed this already, but it's possible to acquire every specialization tech that appears in your tech tree as long as there's an empire in the game willing to trade it to you, and that means that sometimes it might be worth picking up one of the less useful options when selecting a specialization if an empire you know already has the one you really want. -15% manufacturing cost on ships may not be great when you could be getting +10% hull capacity, but if the Altarians already have the +10% hull capacity tech and you're willing to pay what they're asking for it, isn't it better to have both? Remember that if you want to research any specific specialization option, you need to complete research upon that option before trading for another option in that specialization; otherwise, your only option is to hope another empire has developed that specialization option and will trade it to you for a price you're willing to pay (or has traded it to an empire that's willing to trade it to you for a price you're willing to pay, if you didn't turn off tech brokering).
Also, somewhat oddly, you don't really trade your technologies for their technologies so much as you trade slot-unlocks; if I have a tech whose internal name is OrbitalSpecialization1 and you have a tech whose internal name is OrbitalSpecialization2, and you and I trade these techs to one another, I get whatever tech is in my tree that has an internal name of OrbitalSpecialization2 and you get whatever tech in your tree has the internal name OrbitalSpecialization1 even if your OrbitalSpecializationX doesn't do the same thing that my OrbitalSpecializationX does. This also applies to what shows up in the diplomacy window - the techs you can offer to give to the other empire will be called by the name of the tech that the other empire will gain, not the tech that appears in your tech tree in that position, and so the Terran Alliance can sell Labor Exploitation to the Drengin Empire despite no tech in its tech tree being named Labor Exploitation. If you have a tech with an internal name that does not appear in my tech tree, I cannot trade for that tech (thus, it's somewhat inadvisable to create synthetic factions that don't or non-synthetic factions that do use the Yor tech tree; they won't be able to build the appropriate types of farms since the tech trees they're using don't have the techs for those farms, though there is an exploit that I'll mention in a bit that can help compensate for this if you do decide to make such a faction).
If you're willing to have some less great planets wasting some of the bonuses from the 'first X worlds get Y bonus' culture traits, using the first colony ship to colonize the inhabitable world present in most starting systems isn't a bad idea. Hook it up to the local shipyard and even if it does nothing else for you, it's roughly doubling the rate at which you can generate population for new colony ships. Helps a fair amount early on when your homeworld is the biggest manufacturing/research/income producer in your empire, and similar setups can help later in the game when you're trying to build up fleets of transport ships. You can also choose which planets provide the population for transports and colony ships, allowing you to preserve your homeworld's output early in the game or keep the transports gliding out of the spacedocks on the output of a factory world while you drain off the population of a farm world or two.
It's possible to use colony ships or transports to transfer population from your developed core worlds to your newer colonies, speeding the rate at which the newer colonies are developed, potentially increasing your empire's overall population growth (if you're pulling people from max-population or nearly max-population worlds and transferring them to worlds that won't hit max-population even with the addition of the transported population), and possibly improving approval rates (depending on choices made w.r.t. morale-related improvements, technologies, and empire bonuses) which should further speed population growth and also speeds influence generation. More exploitively, this can be used to overpopulate worlds, especially if you have a quick way to generate new population (e.g. one of the Yor assembly projects).
Having a negative amount of a strategic resource doesn't actually hurt you, it just means that you can't build any more of the things that require that particular resource until you acquire enough of it to have a positive amount of that resource or lose/destroy enough of the stuff using that resource to have a positive amount of it. Trade with an AI empire for 5 Durantium and build additional Durantium Refineries or a number of warships using the Durantium mass drivers, and you'll still get the full benefit of whatever you built that used the durantium when the time runs out on your trade arrangement and you end up with -5 durantium.
The trade goods you find on your planets have bonuses that stack, despite each trade good claiming to be one-per-player. Buying up all the Harmony Crystals, Monsatium, Helios Ore, and maybe a few other things with similarly useful bonuses isn't the worst idea ever.
It's possible (and sadly not all that difficult, as long as you can find a bit of elerium and perhaps antimatter), though somewhat exploitive, to make a planet which is completely immune to two or more types of invasion. All you need to do is get a total planetary defense rating of 100% (immune to standard invasion and planetary bombardment), 125% (also immune to information warfare), or 150% (immune to all forms of planetary invasion). An Elerium Defense Shield (EDS) adjacent to a Planetary Defense System (PDS) gets you 100% planetary defense (75% from the EDS, 10% from the PDS, 15% from the 3 levels on the PDS; note that the level bonus of the EDS does not work, and that this is a good thing because for some reason the level bonus of the EDS is currently defined to apply to every planet in your empire, so if it worked you could manage to make your entire empire immune to invasions if you can get 30 levels total on EDSs anywhere in your empire without even needing any other empire-wide planetary defense bonuses, and this is fairly easily within reach with maybe half a dozen EDSs). You can pick up additional bonuses to planetary defense from a few techs (mostly in the planetary defense line in the warfare tree, but I think there's also a specialization in the political branch of the governance tree that gives a planetary defense bonus) or by stacking more levels on the PDS (5 additional levels gets you immunity to information warfare), or eventually by upgrading the PDS to a Planetary Defense Dome (which buys you an additional 40% Planetary Defense on top of whatever you had with the PDS, so 140% planetary defense with just an EDS and an adjacent Dome). "Best" part is that you can render an important world or two immune to all but late-game invasion types in this manner with just a handful of improvements, a couple of strategic resources, and choosing the right two specialization choices (a PDS which is adjacent to an EDS, an Antimatter Power Plant, and a Military Academy will have 6 levels for +30% planetary defense, +10% from the PDS itself and a further 75% from the EDS for 115% total; choosing the +10% planetary defense bonus from the first specialization in the planetary invasion/defense branch of the tree buys you enough for immunity to information warfare, and choosing immunity to Biological Warfare when that specialization becomes available removes the only other threat). Not something you can do for all planets, but certainly something you could do for an important world or two if you really want to ensure that they never fall to invasion. Be warned that such a world can still be culture-flipped, and if it is there's a good chance that it'll be a royal pain to retake it.