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.

It depends on your priorities, hardware, use cases etc. Honestly it’s unlikely to be the determining factor. Available hardware and software support and your attitude to risk are probably more important. Fedora is a cutting edge distro with good reliability and is feature rich. It’s upstream of Red Hat Enterprise Linux so has massive support behind it and a large user base. There are multiple spins if you want GNOME or KDE or an immutable OS etc. Adding additional repos such as RPMfusion make adding Nvidia and other proprietary drivers a breeze. As with most things GNU/Linux you need to be prepared to put in the effort to take control of your digital life. It’s not easy but well worth it.

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

It depends on whether you like your OS to be boring or not. If you like it boring and the LTS kernel works for you, use it.

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

Unlikely. Standard releases are still pretty stable.