Two days ago I completed my best game yet - Krynn with 3 Intelligent AIs(2 custom races and Arceans), 6 Bright AIs, 8 Minor Races in a Rare Stars, Rare Planets, Abundant Asteroids Huge Galaxy with Mega Events, Tech Trade and Super Abilities turned on. The game lasted 7 years and I eventually won a Technology Victory(my first TechVictory) to break the 5-digit barrier for the first time and score 10050 points. I conquered the Torians, Yor, Korath, LentzLandians, Drengin, Nuts(custom), Akilians in said order, allied with the Arceans, Korx and Altarian Resurgance(custom), went Neutral, completed the missile, point defense, armor, engine and more tech branches and built an awesome 2860 tp research-only planet on the former Korath homeworld. By endgame, I was doing a total of ~4500tp of research every week.

Mega Events were the mega spy attack(blocked by my Counter Espionage Centers) and Dread Lords(I won tech victory before I could find them). The races that fell to AI wars were the Paulos and Iconians. Pirates also attacked around mid-game and I found 2 obsolete PreCursor Rangers during late game. I also designed my first top-tech Huge Hulled Dreadnoughts, but never built one - I didn't need to, since my Level-9 Medium and the few Smalls I had outclassed the Korx/Altarian Mediums by the time I conquered the Nuts. After that, the game was practically won anyway.

It's clear(as shown on Wiki page 'Ship Design Strategies') that with a sufficiently fast research capability, nothing beats missiles, so until now, in sandbox games, I've used missiles only - no beams, no guns. Sure, Point Defenses are stronger than Shields but they get worn down faster by higher-damage missiles then Shields get worn by Beams. In battles vs. the Yor, Nuts and Pirates(who had PDs), their balanced designs didn't have enough point defense to stand up to the missiles of my defensively-oriented designs - they were taking more damage than I was.
Then yesterday, I decided to continue the Dark Avatar campaign which I had left off after the first mission. In the second mission, Spies, I had to use Beam Weapons since the other weapon branches had been severely chopped down to only their weakest parts. Since I was the Evil Drengin Empire, I could use the Psyonic Beam. Although I had already captured 2 Terran planets with an older, weaker frigate design, I decided to upgrade my warship with the new weapon before the final attack on the Terrans' last world, just to try out the one-off, ridiculously powerful thing.

The result:

So now I'm downloading the 1.8 update and have created a new custom race for my next Sandbox game - the Bunglers, with Super Annihilator, an Iconian personality and 35 Alignment - Evil/Neutral. Now I'm going to go up to Tough and include 3 Gifted AIs(maybe even setting the Iconians on Genius - they're weaker than other races normally). This is going to be my first Evil sandbox game. But I don't know whether I should:
1. Go for Missiles as usual and have the weak(by Psyonic standards) Psyonic Missile and superior Torpedoes later in the game.
2. Go for Beams to get the awesome-but-overpriced Psyonic Beam, but get stuck with weaker weapons later on (if I don't keep using the expensive Psy' Beam) and end up with the comparatively inferior Doom Ray in the end.
3. Go for Beams, get the Psyonic Beam, then buy a Stinger/Harpoon tech from an AI and research for better missiles from there on. The problem with this is that missiles are expensive to research and I'd have already spent a lot of time to get the Psyonic Beam - but with strong enough research it's not a problem.
I'm leaning towards 3, but opinions wouldn't hurt.