If you do decide to shoot them [and I've been doing it on an off for
years],
get a BB gun that can shoot at a high velocity, use flat-head pellets, and
practice before you go out to shoot them. Squirrels are tough creatures,
and
it isn't easy to kill them with a single shot from a BB gun. If you hit
them
anywhere behind the front legs, they'll likely run away and suffer.
Hitting
them in the head or in front of the legs with a BB also won't ensure a
quick
kill. A flat-head pellet to the chest or head will knock them down, and
you
can finish them with another shot if necessary. I'm a pretty dead shot
with my
BB gun, and can knock a squirrel down anywhere out to about 50 yards. But
I
always use the pellets, and won't shoot if I can't hit the head.

I find that after you kill them pinning them up on a cross next to your
tomatoes as a warning to other squirrels to stay away works really well