When travelling through hostile territory in transports, using a lead and rear empty transport makes the center transports much more survivable. In fact, they take very little fire at all. Just line up your transports pointing toward the first wormhole with an empty in front and back and send them off.
When using Cloaker Starships, Transports make things a lot easier because you can order the attacking ships into the cloaked Transports and they instantly become protected without having to wait for the cloaking timer. For serious raiding, Mark II Transports repair ship inside them, allowing you to repair the incidental damage your raiding force will take without fiddling with Engineers (they become uncloaked while repairing, so you need to back off out of range to use them).
Fortresses can be beaten by removing supply (kill the AI Command Stations on their system and all adjacent systems). Note that Super Fortress does NOT require supply.
Don't try to Missile Turret a Fortress down however; last time I tried this they appeared to have Counter Missiles (in addition to the listed Counter Dark Matter). Use Sniper Turrets instead.
Heavily reinforced planets can be broken by freeing some of the ships in the system (get in range of a Guard Post or shot it) and then backing your fleet out of your system so the AI thinks it is poorly defended. When it rushes in you can counter-attack. Use a Force Field over the wormhole to prevent them from retreating.
Ion Cannons are almost never worth capturing. Use Raid Starships to eliminate them in advance of attacking a system.
You can kill an AI Eye by claiming a system. Kill the AI Command Station with a raid and build your own Command Station. The AI Eye will explode without you needing to kill all the guard posts first.
When using Teleporting units, always group them separately and micro them. Send them in after your other units have engaged and they'll take little fire and live a lot longer. On defense, retreat them to a Mobile Repair Station or Engineers often for quick repairs. You can engage/disengage 4-5 times a fight and still be extremely effective with them. Since you mentioned Bombards, teleporters love killing Bombards
Speaking of Bombards, you want them targeting your Fighters. So if you get a wave of Bombards, put your Fighters (especially Mark I) out there to eat the opening volley, and put everything else in Transports out of range to charge in and finish them off. Riots and Plasma Siege Starships will cripple their engines making it very easy to chase them down.