I highly recommend turrets. HIGHLY, HIGHLY recommend. Much more durable, cheaper and the AI doesn't auto-target them as your first buildings to be destroyed. (With all upgrades, your turrets have 18 armor btw, more than your level 10 battleship. and some great damage and range - again with upgrades)
And for turrets. STICK THEM AROUND YOUR PLANET. They cost 1 slot! One! Ring your planet and then stick some more around likely angles of attack and the locations you have your logistics buildings.
2-3 Repair bays. 2-3 Hangars. 1 Shield generator. 12-18 turrets. It works a charm (and theres no easy counter, unlike human players who can just build a huge fleet of carriers, build a ton of fighters and jump insystem and oh look, your hangar defenses just got invalidated if you built nothing but hangars.
He can't rush your planet cause of the shield generator... he can't just go after the shield generator (he'll take a pounding by all your turrets the whole time). And it takes forever to clear very many turrets. They have a LOT of hp and armor. All of which helps you buy a LOT of time for your fleet to get there and sandwhich them between your defenses and your fleet.
No, turrets won't kill ships jumping around the edges of your system, no turrets won't rape capital ships. But they aren't as easily countered, they'll hold your position longer (to wait for your fleet to jump and in smash his) and at the end of the day you'll be left with a lot more of them and a lot more money to buy more defenses.
The short version. Two turrets. Roughly 9000 hp with all upgrades. 36dps Two tactical slots. 500 credits, 250 metal, 100 crystal. What part of this doesn't sound like a good deal?
I'm talking for TEC anyway, Vasari/Advent turrets slightly different

(But still follow the same strategy pretty much)
As for your fleets... don't spread them out. Keep a couple scoutships around to keep up with things but group your ships together... have a defense fleet and a offense fleet. Otherwise you'll get destroyed piecemeal. Enemies will run from larger fleets (thus you don't have to replace units) or fight it out... and lose a few/potentially all... whereas if you have just a few units and keep sending small groups of units your GUARANTEED to lose a few or potentially lose them all anyway.
The Vasari Nano Weapon-Suppressor or whatever it's called runs out of antimatter fairly quickly for my tastes. I think it should be a constant area of effect, or have a reduced cost and cooldown.
Its worthwhile once you get the multiple ships affected at one time research for the supressor