What the best weapon? I been using railguns mostly.
There is no best weapon, though lasers seem to be the most popular.
Missiles are the most versatile and the most powerful, but they're very expensive.
Particle beams can have great range for very a relatively low weight and cost, so long as you improve the range tech. They also deal full damage at max range, unlike all other beam weapons.
Plasma carronades are only good very early on, since they start with a higher damage than the other beam types (more bang for the research cost). Beyond that, they have terrible range and fire slowly. Their penetration is also as horrible as missiles.
Railguns have the best damage output and are reasonable for anti-missile work.
Lasers have high range, decent damage, and great penetration.
Gauss cannons have terrible range but their high ROF makes them fantastic anti-missile weapons. High-ROF gauss can shred ships, too. If you use beam fighters, gauss cannons are a good choice despite the accuracy penalty (since only small ones will fit on most fighters).
High-Powered Microwave has less range than a laser and deals a single point of damage. However, it deals 3 damage to shields (yay?) and ignores armor. It only damages electronic systems, so they're best used to cripple ships for your other warships and/or boarding parties.
Meson cannons have the same range as microwave IIRC, deal a single point of damage, but ignore shields and armor. In large numbers, they're wicked. These are another great choice for beam fighters.
So, yeah... It depends on what tech is available (from salvage or whatever) and what your needs are. If you can afford missiles, they're fantastic. I'd save 'em for your main battle fleet(s), your homeworld, and emergencies. If your enemy is heavily shielded and armored, railguns and mesons are great options. If they have light-to-moderate armor, high-caliber lasers can punch right through it. If your ships are faster, feel free to plink away with particle beams at long range. If you plan to capture enemy ships with marines, use microwaves after tearing down their shields with something stronger. And so forth.
Take my suggestions with a grain of salt, though, as I'm a terrible player.