Don't forget that fighters are good at taking out other strike craft (i.e. fighters and bombers) as well.

I lurve bombers. Just person preference and based on my playstyle, but I typically most almost all bombers with only a few fighters to help keep them safe.

Bombers typically do well against the heavier ships and buildings. Other than the obvious like heavy cruisers, I like to use them to spike an enemy capital ship or to blow one up as it tries to run. It can be hard to catch a fleet with a standard fleet of your own, but strikecraft have no problem closing the gap and laying down some hurt before they bug out.

fighters do anti-light type damage which is especially good against bombers, siege frigates, and long range frigates. it also does increased damage (though slightly less) to fighters, and civilian ships (trade ships, colony ships, etc.). it does greatly reduced damage to everything not on the list though.

bombers do anti-very-heavy type damage which is especially good heavy cruisers and orbital structures. its also pretty effective against capital ships, and other support cruisers. its decent against everything though, because bombers have very high damage anyway so against the stuff that they technically only do 50% damage to its still a reasonable amount.

fighters are uniquely well suited to attacking bombers and fighter squadrons for an additional reason though. All ships except fighter squads and flak frigates only have a 10% hit rate against squadrons but fighters have something like an 85% hit rate.

1) Bombers and fighters move at insane speeds, so they can intercept enemies faster than anything else.

2) With the exception of Flak and other Fighters, there's only a 10% chance of an enemy even HITTING a Fighter or Bomber, and if the odd one is lost, they are rebuilt quickly. The sum is, that the fighters and bombers themselves are virtually impervious to attacks from a fleet that isn't specifically prepared to counter them.

3) Fighters are meant to counter Light and Very Light vessels. (That means other Fighters and Bombers, Long-Range Frigates like the LRM, Planet Bombers, Scouts and Colony Ships.)
Bombers are strongest against Very Heavy (That's Heavy Assault and planetary Structures) and Capital-ships.
...neither does particularly well against Medium (Basic assault frigates)and Heavy (Support Cruisers, and Flak)

4) The starting Ratio that I would go for for maximum versatility, which naturally needs to be ammended if the opponent does something un-expected, would be 1 figher to 2 Bombers. The reason is, that Bombers do *Reasonably* even against armour-types that they are not designed for (50% Damage against anything Very Light to Heavy), so they are the most versatile of the two. Fighters, on the other hand, are fantastic against the targets they were specifically designed for: Light Armour, where they do 200% damage. Noticably, the 2 major vessels in this class are Planet Bombers and Long Range Missile frigates, which would be EXACTLY the class of vessels you would want to get rid of quickly when attacking or defending, respectively. Against Light, 1 fighter-squad is worth 4 Bomber-squads.

5) For the reasons in #4, I can only echo what AmishMonster wrote above me: Fighetsr are for defense, Bombers are for offense. A few Bombers can't stop an attacking fleet anyway, but a few fighters CAN kill off a group of Planet Bombers.

(PS: There's an ongoing debate on whether or not Planet-Bombers are worth it, compared to using an Anti-Planet Cap-ship. The consensus seems to be that the Cap-ship is the best way to go by far, and if your opponent agrees with this, fighters become slightly less relevant as a defensive measure. The computer AI, however, still seems to favour Planet-Bombing Frigates, so in non-Multiplayer games, you should still favour Fighters for your defensive hangars.

I do believe that they stay. So even if you kill off the Hangars or Carriers, you still need to swat the flies.  

The fighters start to slowly die off. They don't vanish right away, but they do eventually disappear without a support structure/ship.