Used saws typically require more maintenance at first unless you get lucky.
Clean exposed metal with compressed air, especially the cylinder fins, flywheel fins/ignition module, recoil cover, the case under the muffler, and between the cylinder and fuel tank. Crud traps heat.
Check the tune. 13,500 rpm max high speed with a tach, or 4-cycle changing to 2-cycle in the cut. The idle is typically rough on a 440 because of the light flywheel, but if it idles without stalling or spinning the chain, that's ok. With a sharp chain, a 440 should cut wood with a vengeance if the top end is ok.
New fuel filter, spark plug & Stihl HD2 air filter if it doesn't have one.
Remove the clutch drum and clean/lubricate the needle bearing.
Check fasteners for tightness, particularly the one connecting the top cover to the cylinder. Too much torque can pop the boss on the cylinder. Not enough and the screw can vibrate loose and mess up the threads.
Listen while the saw is accelerating; no metal or bearing noise.
Find a parts and service manual. You'll need them sooner or later. PM me if you can't find them online.