Have you read the Bombing Guide on the wiki? It's pretty good.
Because of your remark about damage types, let me point out: Damage type is not the most important criterion in choosing a bomb (unlike in swords and guns, arguably). There are a couple of reasons. First, the support bombs are used for reasons other than damage, such as status, vortices, knockback, etc. Second, bomb blasts often hit monsters of multiple families, and you can't expect to get special damage against all of them.
Now here is my standard "so you want to try bombs" advice:
* Dark Briar Barrage and Dark Retribution are damage-oriented bombs. They are easy to use because of the lack of knockback.
* You should try a haze-style bomb. They're all good except for Shivermist Buster (in my opinion). People usually think of them as support, but there are situations in which Voltaic Tempest or Ash of Agni can inflict massive damage.
* You should try a vortex bomb. Most people say that the shock one is slightly better than the poison one, which is significantly better than the original one. But any of them would let you try out a vortex lifestyle.
There are more bombs than that, of course. Eventually you should try all styles. But the ones above are the natural first choices for someone with your background.
