LTS kernels aren’t more or less stable. Rather, they have been selected by the kernel maintainers to get security fixes backported to them for a certain time.

Ubuntu does the same thing for the kernels on their LTS versions (technically they usually are not LTS kernels since canonical supports them instead of kernel team)

Overall I’d suggest going with what the distro provides unless you have very new hardware, in which case a newer kernel may be required

At home it probably isn’t worth it. Servers where changes can break things or is qualified against a specific configuration, more worth it. Often whatever your distro is providing is fine, even things like Ubuntu and soon Mint will be using non-LTS kernels by default.

How likely is my system to break with the standard kernel?

Unlikely. Standard releases are still pretty stable.

LTS just means Long Term Support in case you weren’t aware. It means no new development is happening, but security exploits will be patched as soon as they arise.

If you just want stability, LTS is the way to go. If you want all the cutting edge bells and whistles and are okay with potentially some instability (but probably not much) then use the latest version.

If your device isn’t connected to the internet during general use then I wouldn’t worry too much about updating anything. Security fixes aren’t important if there’s no way to connect to your device.

Depends on the hardware you have. The fact you’re asking this means these latest features wouldn’t mean anything to you. I doubt you’d actually notice any difference.

My advice: use the LTS kernel if that’s what your distro provides, only change if you find some hardware not working.