I am also fairly new to the game, but have found the there is little to fear in caverns if you are sufficiently cautious.
I wall off my first cavern strike and then build a long-ish tunnel 3 wide that hits the cavern at a fairly level spot. In the tunnel goes 2 raising bridges that can seal off the fortress when a forgotten beast arrives. I leave as long of a stretch as I can in between them, and put a wooden door in there somewhere, just empty against the wall. The distance critters have to cover, combined with the attractive power of the door to building destroyers, gives my dwarves the maximum time possible to react to the "pull lever" command and trap uninvited guests between the bridges.
In between the bridges, I put a long perpendicular corridor (again: as long as possible because dwarves sometimes take forever to pull the levers) that has its own sealing bridges and which connects with my fortress at a second point. This corridor is only 1 wide and full of steel spike traps connected to a single lever. This normally remains sealed.
This is the FB trap. When a FB arrives, it gets trapped in the 3-wide corridor, at which point I open up the secondary entrance. The FB then tries to path into my fortress through the trap, and gets caught again between the two bridges, at which point the spike traps can be triggered repeatedly by putting "pull the lever" on repeat to kill the FB.
It's low-tech - there are better ways to automate a repeating task, but time is not of the essence when the FB can't leave the trap - and the time required to complete this setup is minimal. No military is required to deal with the FBs, which means that even deadly-dust FBs can be handled safely. If you complete this setup before breaching the cavern the second time, the risk to your dwarves, while never zero, is minimized.
Caverns are pretty awesome. They are a good source of high-quality meat and leather - giant toads and giant olms are easy to trap and easy to train, and have a 4x butchering modifier. Cave crocodiles also produce high-quality meat, and also eggs, and they can be domesticated. Once you hit a wet cavern, your muddied stone and underground soil layers will start to sprout floor fungus, which allows you to keep your grazing livestock underground. A single giant cave spider can produce effectively limitless quantities of high-value silk with the correct setup. Ordinary cave spider silk is almost valueless, though, so I would add a "Collect webs" task to your loom and suspend it, so your weaver doesn't keep going to the cavern for it.
Caverns are like the aboveground area, in that generally only 1 group of a single species of critter will be present. I have seen this violated from time to time and I don't know why it happens, but if you find a giant olm chillaxing in the middle of a pool you are probably safe exploring the remainder of the cavern and setting up traps to capture desirable critters, leastwise until the olm decides to move on.
Good luck!