basic guidelines for fleets and combat:
1. the main offensive ship in the early game is the Long Range Frigate, it should be the backbone of your fleets until you have a robust economy. once your econ can support them, carriers are the best offensive ship you can buy.
2. the main offensive ship in the mid and late game is the carrier cruiser. bombers are devastating against enemy structures, capital ships, and heavy cruisers. fighters are very effective against enemy long range frigates and support cruisers and are also the best defense against enemy bombers. in the lategame the fleet with space superiority (meaning the most squadrons) will almost always be the winner.
3. light frigates (like the Cobalt) are just not very good. they rapidly lose utility after the first 10 minutes. once you research the anti-matter draining ability (Steal Anti-matter, Sabotage Reactor, etc.) light frigates can take on a specialist role of countering enemy support cruisers.
4. anti-squadron frigates (like the Garda Flak frigate) are very durable and very good at shooting down fighters. they shouldn't be used in large numbers but a few go a long way, especially if there aren't a very large number of squadrons in the opposing force yet. they do get outclassed against lategame fleets though and ultimately you'll rely on your own fighter squadrons instead of flak frigates to clear the skies.
5. cap ships aren't very good unless their abilities are well developed. learn the ins and outs of each cap ship ability to improve your performance. it can make all the difference in the world. also don't trust the AI to properly use your cap ship abilities, micro managing cap ships will boost performance by alot. a well played cap ship will dominate a battle. a poorly played one isn't noticeably better than the equivalent fleet logistics deployed as boring old Long Range Frigates.
6. a small number of support cruisers (such as the Hoshiko and Cielo for TEC) make a HUGE difference in combat performance. don't underestimate just how powerful those special abilities are.
7. siege frigates are very expensive and very fragile. they are generally a waste of money and fleet capacity in the early and midgame but will become necessary in the late game when you are more likely to be assaulting multiple planets at once. cap ships are better planet killers (particularly ones with anti-planet abilities like the Marza's Siege Guns) but you just won't have enough cap ships to be at every planet you need to bomb.
8. the best way to defend is with a frigate factory and a repair bay. leave some fleet capacity available and build ships in response to being attacked. if you succesfully repel them your counter-attack force is already built! this technique also lets you build the most effective counters against your attacker instead of having to guess ahead of time what you'll be attacked with.
9. some planets aren't worth defending. it might be better to just let them go and re-colonize later. you might just use the opportunity to scope out your opponents fleet and build some good counters and then go after him. or you might out-flank him and take out one or more of his planets while his fleet is busy taking out a planet you didn't care much about.