Do your best to keep your starbase alive no matter the cost. If that means sending flak frigates into the area to act as meat shields, so be it. Make sure to have a few Hoshikos around your SB at all times as well.
I, for one, always avoid building starbases in neutral gravity wells like Gas Giants because they're difficult to repair effectively. In a neutral well, they can be repaired at most at a rate of 20 hull/sec: but if you have a SB on your own world with repair platforms you can repair it at a max rate of 60 hull/sec, which will nearly always be enough unless you're fighting Vicious with extremely huge fleets.
I followed the fleet that jumped earlier. The planet they jumped to turned out to be their capital world and it was heavily defended (not surprised). I found myself facing overwhelming odds so I had to pull my forces back. In fact, I had to pull them all the way back to one of my worlds because they followed me back to the world I bombarded and then to the gas giant.
Always scout before you jump your primary combat fleet into an unknown gravity well! You usually don't want to engage in a battle you'll have to retreat from!
The capital world defenses consisted of at least four hangars so I experienced a very thick cloud of SC activity. The enemy fleet that tore through my fleet and chased me away included several capital ships and cruisers, I think.
Flak effectively counter fighter strike craft. You might want 5-15 or so, depending on how many enemy SC there are - they'll rip fighters to shreds easily, and will do some damage against bombers as well.
How effective is the heavy cruiser? I have (or had) at least 20 of them. I have plans to construct another 20-30. I also plan to increase the number of carriers by 40-50 with an even distribution of fighter and bomber squadrons. I normally build LRM frigates, but I didn’t this time. I read that they are effective against other frigates, but how do they fare against about cruisers and capital ships? I want to include torpedo cruisers, but I fear they will be destroyed before they can bring down the hangars.
You're TEC, so that affects things.
Heavy cruisers are good against all ship types, but are quite weak to bombers.
Since the AI is prone to building LF at all stages in the game, it's a good idea to have at least a few LRF (for you, LRM) in your arsenal. LRF are somewhat difficult to counter effectively, even by human players. Long range frigates do some of the most damage for their cost, against all enemy unit types, including cruisers, capital ships, and structures. Unless you're facing extremely powerful AIs like Cruel and Vicious, a fleet composed almost entirely of LRF can often win you the game.
If you like torpedo cruisers, don't be afraid to build them - they have such a large range that the AI will rarely be close enough to auto-attack them. If the rest of your fleet is in front, your torpedo cruisers should have no problem surviving.
Another way to easily have a very powerful fleet is to focus entirely on carriers with bombers (no fighters). Fighters are only really that effective against enemy bombers and don't do all that much damage; fighters die way too easily to enemy flak (even enemy AI flak) for me to build fighters past the beginning of the game. Bombers do much, much more damage against nearly everything, including enemy capital ships, structures, and heavy cruisers. As Darvin suggested in an earlier thread, a rule of thumb is that if you can build 100 bomber squadrons against the AI, you've won, because your fleet has so much firepower and even the hardest AIs have no idea how to deal with them.