Well, I think it's a matter of simultaneously keeping in mind the tactical objectives as well as the overall strategic objectives. At the lower/mid difficulties, you can win without worrying too much about the other races, but just focus on your own colonies and your economy/teching, sort of like a space version of SimCity. At the higher difficulties, though, the computer races get a lot of production advantages, and the pace of your techs is much slower (each tech is twice as expensive on impossible compared with on simple) while it's faster for them (due to their production), so you have to be able to deal with them much more on the higher difficulties.
In your saved game you did a good job of expanding and building up your resource base, it was simply a matter of converting that into military power. You already had the highest population, and you were keeping up with production. I basically used some of the production to make a huge bomber to take care of bases, and then used the population for invasions. It's true that this will initially be very costly, because you didn't have much ground techs, so I made sure to focus on ground techs in my construction, force field, and weapon techs. Once you're able to capture a few colonies, the tech boost that you get from them should allow you to make much better ships.
Once I start doing a military, I tend to use huge ships with auto repair; they are hard to kill, so I don't waste resources having to replace my military (other than to upgrade). I typically also try to get improved space scanner relatively early so I can see when ships will arrive at my bases, and I generally won't build bases until I see a ship coming (unless the colony needs a lot of turns to build them, in which case I will build them beforehand). This way I'm not wasting resources building and then maintaining stuff that doesn't get used most of the time anyway. If I get into a war early on then it'll be large ships instead of huge ships, but my chance of losing them is higher.
My huge ships will tend to be a laser ship of some sort with warp dissipator and heavy (2-range) beam weapons to take care of ships, and either bombers or missile carriers (depending on what techs I get) to take care of bases. I'll also make some large ships that are pretty much just extra warp dissipators with some heavy lasers to help defend against minor attacks.
And yeah, to capture bases, I tend to send several troops from many different colonies and have them converge on the target colony on the same turn. I don't recommend it for everyone though because it takes a lot of planning and risky: if you misjudge how quickly you'll wear down their bases, you can lose several hundred troops to enemy bases this way (which has happened to me before). It also takes a lot of planning and intricate detail to carry out sometimes, so each move takes a long time. But when it does work, your colonies are still nice and strong, so it doesn't affect each individual colony as much.
I went back and replayed the last few years, and made an animated gif of the between-turn animations of my troop movements for several turns, so you can see this in action:
To the west, you can see Cryslon (yellow star) being taken over in 2487, followed by Maretta to its northeast, then Pollus to Maretta's north, then Kailus to Pollus's west (northwest of Cryslon). Each time you can see ships moving before the troops arrive; that's my bomber taking out the bases. Actually I mistimed things on this one, the troops arrived one turn later than my bomber (if I timed things correctly, they would've arrived on the same turn my bomber arrives), so I should've just kept the bomber there an extra turn, but oh well. That one turn between when my bomber kills the bases and when the troops arrive, if my bomber already left for the next target, means the target could build bases to destroy my troops in the meantime (and I think the Silicoid did, just not enough to prevent capture).
The same thing is happening to the Bulrathi in the east. It might be a bit harder to pick out but I first capture Uxmai (green star in the southeast quadrant) in 2483, followed by Moro and Galos (the two stars north of Uxmai) simultaneously two years later, followed by Ursa to their east two turns after that, then Xudax (red star in east) the following year, then Artemis (white star in the east) two years after Xudax, along with Nazin (southeast part of north nebula) and Rana (south of Nazin near middle of map). Each of those captures was planned out around 3-5 turns ahead, simply because it took that long for troops from my southern colonies to reach them. It might be harder to see though also because I had my western colonies send extra troops to my eastern colonies to beef them up, before more Silicoid colonies became available to capture.
You don't need to do this on impossible, and I don't recommend this for everyone; in fact this is somewhat overkill (trying to plan out multiple invasions simultaneously and spreading the load between all your colonies) here. I did it here because I was already in the mop-up stage, with my "unkillable" huge ships already made, and I was trying to hit them one right after another as fast (turn-wise, not "real" time) as possible. Realistically though if you're at this point then you can win any way you choose, and just having a single death fleet kill the bases at one colony and hang around while your troops from nearby colonies arrive will work just as well (and is much faster to execute). I tend to be perfectionistic when I play though so I'll plan out most of the details, but it means each turn at the later stages can take hours if I'm handling multiple invasions. At the beginning parts of the game though, when you're trying to score your first invasion against a better enemy to get their techs, it's helpful to plan out your troop movements and spread your troops from across multiple worlds so that you can muster nearly unstoppable numbers onto a single target colony. In the animated gif you can see multiple sets of troops starting to converge on a planet, and my nearby colonies add to the wave as the transports pass them, resulting in a lot of troops arriving at once on each planet.
Oh and typically I think the militaristic races are somewhat harder to play, since generally you don't want to be engulfed in war too much so the bonuses don't help you until you are -- but then you don't get the econ benefits that compound over time. I'm not sure what else to say about that though, other than that yeah generally they can be somewhat harder.
