I personally bomb quite a lot since I crafted volcanic demo armour and some decent bombs.

For your first bomber armour, I would definitely recommend Volcanic Demo Armour. It has charge time reduction and fire resistance, which are both fantastic for any kind of bomb. It really helps in the later levels as a lot of them are fire-themed. Get crafting bomber armour right away!

As for the bombs themselves;

Blast bombs are your standard kind of bomb for doing lots of damage to lots of things at once.
The main one to go for is Dark Briar Barrage (The snarbolax bomb) as it is effectively a piercing nitronome without the disruptive knockback, making it very valuable for damage-bombing in teams.

I find that blast bombs really shine when other people are using bombs too. If everyone in the party is using nitronome, monsters can't ever get close (and with sufficient damage boost, turrets get interrupted) and the game becomes pretty easy. But barely anyone uses bombs, so this scenario is pretty uncommon.

Shard bombs can be fun to use, but are fairly weak in the grand scheme of things. They're also quite hard to use due to their erratic knockback. Avoid them for now until you gain more experience with bombing and want a challenge.

Haze bombs are fairly situational, the fire version is fairly good for doing constant damage if you can kite monsters through it well, the poison one helps deal with healers, shock and freeze can help with crowd control, but might disrupt teammates as Bopp rightly pointed out. It is useful to keep them in mind, but I find that I usually end up just taking a more damaging bomb anyway.

Vortex bombs are very useful and powerful in groups, it allows your teammates to focus their attacks easily. If you can, try to go for the electron vortex, but this requires playing lockdown or blast network which can be difficult. If this is too much work you can get a graviton vortex instead, which will still group things together fine.

If you can get Operation Crimson Hammer, the bomb you get from it (Dark Retribution) is absolutely fantastic and should be in any bomber's arsenal, in my opinion. It's very very strong against all kinds of enemies.

As Bopp said, the bombing guide on the wiki is very good. The wiki is having some trouble recently so apologies if you can't reach it.

I would also suggest you browse the Shard Squad youtube channel, as Zeddy has posted a lot of bombing-related content on there. I found it very useful for picking up techniques and general bombing practise, as well as gear setups.

Happy bombing!