Beams are medium rate of fire, medium damage, high accuracy, medium range.  Missiles are low rate of fire, high damage, medium accuracy, high range.  Kinetics are high rate of fire, low damage, low accuracy, low range.  All of those are just the "normal" states for the weapons.  With various techs you can substantially alter the characteristics of each weapon type.  I would say all of them are viable, it is just a matter of your personal preference.  Of course resources can also let you build enhanced weapons.  Elerium lets you make enhanced beams, anti-matter lets you make enhanced missiles, and durantium lets you make enhanced kinetics.  Durantium is usually the most common of those resources, so it can be easier to make lots of ships using enhanced kinetic weapons than it is to make enhanced beams or missiles.

As far as the balance between the different types of defenses (armor, shields, point), those are all relatively the same.  Armor only works against kinetic attacks, shields only work against beam attacks, and point defenses only work against missile attacks.  So the one that is best for you to use depends entirely on what weapons your enemies are using.

Hope that helps.

Some races do favor one over the others. Drengin favors Kinetics, for example. However, most races will use what they perceive as the most damaging weapon in the situation, so they will even adapt to balance changes without being told to.

Right now I'd say that kinetic weapons are usually the best of them (unless your opponent has a high jamming value, which exacerbates their poorer accuracy) since their damage is actually quite good for their size and with the rate of fire module they shoot fast enough to overpower just about anything; the one exception is that the elerium beam is easily the best special weapon type (while the antimatter missile is the worst).  Add an accuracy buff to your faction, and kinetics become amazing very quickly.

In my experience the range buff that missiles and beams get over kinetic doesn't amount to much, even if you don't mount thrusters.

Also I have not seen the AI adapt to weapons yet.  They tend to favor shields and chaff, probably because they're smaller than armor modules.  However they will continue to use (and even upgrade) their shielding and chaff if you were to exclusively use armor.  This is probably changing in the next few patches but it hasn't changed in the beta patch (1.10) yet.