My impression is that you are reading a lot of information, some of it seems contradictory,
and it is confusing you as a first time BB installer. Welcome to the internet.
If you stop and consider for a minute or two that your BB and the crank arms that attach
to them are pretty high load areas on your bike (you push down on the pedals with some
of the largest muscles in your body, and sometimes you actually stand up and apply full
body weight), you'll better grasp why both the cup interface with the shell, and the
crank arm interface with the spindle need to be torqued down relatively tightly. Thus the
need for a tool that provides more leverage than your hands.
Having said that, you will encounter much conflicting opinion on grease/no grease, and
the importance of an exact torque. I personally always grease or use anti seize on anything
threaded on a bike that i assemble. I usually leave the taper faces on the shaft dry, but
have been known to grease those too, if there is an issue with use in very wet or otherwise
corrosive conditions..........it really does not seem to make much difference. I also grease
the threads on the crank bolts........like I said, every threaded interface.
I have several torque wrenches and never use them for this. I pull the cups as tight into the
threads as I can with a sealed unit BB, without destroying them.........often one or both are
plastic now, so stripping it is a potential problem.
I honestly don't know anyone who uses a torque wrench for a standard square taper BB, but
I do use something for external bearing cups where bearing preload, or excessive bearing load
might come up as an issue. Again, I have a personal bias against external bearing cup systems,
both because of the costs (usually higher) and the issues that can present with spindle length
and chainline.
Mostly, try not to overthink this.......and if you feel any looseness at all when you are pedaling
around, stop, determine the source, and retighten everything. Most damage happens when
people ride around on them loose.