Your ship design could be a bit better, I think. I've only gotten around to watching your setup video now, but what strikes me is that you're essentially building space snails with guns. Cruise speed 11? That's really slow. Turn rate 10 degrees isn't nimble either. It might feel like 99 firepower is a lot, and indeed it isn't bad early on, but epsilon torpedoes are not a good enough weapon, in my opinion, that you get the necessary bang for the very severe amount of bucks you're paying in production and maintenance costs. A more nimble ship could stay out of range of enemy weapons a lot better, thus surviving a lot better, and that in itself would probably be enough to get the job done until you get more worthwhile tech.
Also of note, your energy economics just barely work out that you can move and shoot at the same time, though "move" is perhaps a bit flattering at speed 11. Generally, you'll want the sum of your engine cruise energy requirement and your weapon energy per second to be less than the excess energy output of the reactors. In your case, you're five over, which means you'll be draining your energy storage during long engagements. It's not really a problem at a mere five but it isn't optimal either.
And finally, what's up with your Gerax drives having warp speed 7000? That's definitely not a vanilla setting. Are you using "beyond extended" or some other tech mod?
Oh, and before I forget, you do not actually need troop modules on destroyers and the like, but you can in case you like dropping off raiding parties. When playing as a regular empire, I never bother with troop modules on anything but dedicated troop transports, but of course you might want to move troops on your combat ships. If so then I would delay designing ships with that capability until you actually start raiding colonies so that you don't pay maintenance early on for a capability that you're not using. This game rewards a cost/benefit approach to certain questions. Like, "what is the cost of adding this component and what is the benefit?", and if it turns out that there is any cost and zero benefit, well...
I know you don't want to crush yourself under the weight of too many details but early game micro does wonders to give you a good start.