Is it normal for a ball valve to drip as a result of using it and then
stop
dripping? If not, then do you recommend I get any work done on the main
shutoff valves if the nuts holding the handle get wet as a result turning
them?

Ball valves "usually" can't be adjusted and "usually" there is nothing you
can tighten. But just as in a more conventional valve there may be
something you can tighten. You may have to take off the handle using the
obvious nut to see if there is anything you can tighten. If there isn't
anything you can tighten and the leak doesn't stop itself after a few hours
you might was well replace the valve.

Since you have "public" water, you might check NOW to see how you can turn
the water off at the meter.

We own a house on public water and the water company doesn't have any
problem with us using "their" valve. That don't want us to break the wires
for the electronic meter reading but otherwise.... The local "big box"
store sold "Keys" to operate the valve for less than $10. If you have long
arms and strong arms you can operate the valve with an adjustable wrench.
I decided to pay the $10 for a "key."