A lot of people advocate the "artillery hold" for springers, but I've had fine results with a normally firm hold that you would use on a low-recoiling rifle. The worst thing about the typical break barrel is the separation of barrel from scope, which isn't a problem if you shoot irons (both sights on barrel). I have a $100 gamo that was horrible with a scope, obviously because the barrel would never exactly line up upon reloading. Shooting with irons in that gun simply hammers the red squirrels as a springer (actually nitro piston) pushing a 22 around 900fps. An accurate 177 going even 500-600fps will do the job when close enough, i.e. <20 yds, although I've killed pests at 50yds with a 600fps pumper and a lucky shot. Step up to PCP and destroy all pests within 50 yards, and some at 100!
