Tier 1 danger rooms are the place to start and practice. Once you're comfortable there, try them in the top half of tier 2, then the bottom. Basically, work your way down slowly. Don't worry about what gear you have. With the right skills, you can defeat any T2 danger room in 2-3* gear (although it will be slow). It's only 3 energy to enter, so try them out, starting as shallow as possible, and see what you can handle. It's better to try and fail than to avoid the challenge because a random person on the forums told you to get expensive equipment first.

As you noticed, bombs are very useful. I like the knockback of the blast bomb and spine cone lines to help keep space between myself and the mobs (don't use the spine cone in a jelly room). If you have a party of 4, that can get pretty chaotic, though. I usually go in a party of 2 and my partner is used to my bombs, so blast bombs have worked very well for me.

The fiery vaporizer line is great (as long as there are no oilers) even before 4* if you know how to "kite" enemies so they follow you through the mist. The damage it does is amazing and with no knockback it's safe to use with a full party. Freezing vaporizer is also good, especially in a party where your swordfighters will enjoy the chance to swing with impunity. Freeze bombs can be dangerous in danger rooms and arenas, though, because if you place them wrong, you can trap yourself or your teammates by freezing enemies around you. Toxic vaporizer and haze bomb lines aren't really worth it (unless someone else in your party already has fire and freeze) because the poison and stun they inflict barely lasts long enough for two sword swings.

I also don't mind guns in danger rooms. Alchemers are good (although not against wolvers and gremlins), especially at the 4-5* level because of the ricochets. Pulsars are good because of the explosion, but can cause chaos akin to blast bombs when they explode, so use them carefully or when solo. I had a decent experience with my toxic catalyzer, too. Although it was much slower than bombs, I was able to keep enough distance that it was safer.