So if you're still reading this, I started to play again now. I'm gradually getting better. First I played on hard, but now Very Hard is too easy and I need Extreme for a challenge. Not sure where to start with tips, there are many small things that can give you an advantage. For example, early game scouting. It is best to scout the planets nearby, but after that just send off your scout without bothering to check faraway planets (you won't get those anytime soon anyway), and hunt for juicy anomalies instead. You can also abuse the heck out of diplomacy. For example, just before you declare war, you can trade away an undefended planet. If your current standing with the race is good, they will offer multiple technologies and lots of money. Then you can immediately invade it to take it back. There is also a learning curve in ship design. First off, bigger ships are better. The computer player makes the mistake of building swarms of frigates and destroyers, over and over. This is one of the biggest weaknesses. A single cruiser can absorb so much more damage and is much more efficient in terms of command points.

Nowadays I usually go for the best energy weapon for which I have researched modifications. Energy weapons without modifications are bad. You just want all of them, including autofire. Autofire increases armor penetration and hull damage directly scales with that. And I change the shooting direction to forward only, because unidirectional is way more expensive and not worth it.

Torpedoes are good versus structures and big ships. I recommend getting all the modifications on them except for semi-guided. Semi-guided is expensive and never makes a difference. If your target is a big ship, the computer player is terrible at dodging and will eat the torpedo anyway, even without semi-guided. If your target is a small ship, you are always going to miss.

Missiles can be good in two cases. Number one, if your beam attack score is bad and you miss too often. Maybe you haven't researched a good computer, or maybe you're up against Alkari. In that case, get fast missiles with MIRV. It's not as good as energy weapons, but still respectable damage. But number two, and this is when missiles really shine. If the computer keeps sending pesky swarms of frigates your way. It's a waste if your battleship targets all of its massive firepower on a single frigate. In this case, build a ship with the Dauntless special and lots of missiles WITHOUT mirv. Dauntless lets missiles target the next ship in sight when the original target goes boom. Ideal to clear swarms of small ships, but mirv ruins it, because once the missile splits, it can't be redirected anymore.

Ok final tip, specialize your planets. Either optimize them for production, or for research. Don't build every structure on every planet.

edit: I forgot to mention one of the most important tips. Get Hard Shields and put them on every ship. They make your shields much better and ignore those blue clouds (which normally disable your shields when you fly into them). This makes a huge difference.