Though I agree that the Lycoming 360 series, and perhaps other engine types, do permit, and provide information for, "over square" operation (MP in inches higher than the RPM in hundreds), there are other engines for which this is certainly not a good idea. When not approved for the engine, you are treading into detonation territory running over square, and the bad outcome of that gone wrong is really bad, and quite quick. A friend melted two pistons in his C 180 doing that on a hot day.
As long as you familiarize yourself with the permissible power settings, you'll be fine. If in doubt, don't operate a normally aspirated engine over square.
Avoid rapid movement of the propeller control, particularly when moving from course to fine pitch (RPM increase). Rapid movement of the propeller control into higher RPM, with any amount of power being developed can result in the engine momentarily overspeeding. Overspeed is possible during takeoff if you slam the throttle up - be gentle. I once had a Cessna 340 engine overspeed just at rotation on takeoff, I had to move the propeller well into the Low RPM setting to keep the engine within it's limiting RPM range. It worked, and I flew it home that way, as no maintenance was available at the departure airport.
On the other hand, on a warm day, and with due consideration for the possiblity of shock cooling, or other engine temperature excursions, set the plane up in a safe glide. With the engine at idle, slowly move the propeller control toward Low RPM. You'll see the change you can expect, should you have an engine failure, and you choose optimize your glide that way.
Also be aware that at low power settings and fine pitch, the RPM might sit right in the yellow "avoid" range. Coarse the prop a bit, and it will drop below that engine speed.
When flying the Arrow, familiarize yourself with the possible installation of the automatic gear extension system. Many Arrows had it disabled, though some still have it. If it is there, understand it, and how and when to lock it out. Be aware that if it is there, it will prevent you from retracting the gear at a lower speed, which can surprise you in a bad way on rare occasions.
If the Arrow is a turbo, be very certain to not overboost it when applying takeoff power, and be certain to idle the engine for two minutes after you're finished taxiing in after the flight, to cool the turbo, before you shut it down. Be wary of enthusistic people walking toward the plane as you do this.
If it is a "T" tail Arrow, they are very nice to fly, but get some training on landing and takeoff if you've not flown "T" tail Pipers before - they are different.
When you move on to the next phase of constant speed props, and start to fly twins whose props can be feathered, remind yourself that if you have an engine failure, and you let the engine stop turning, you probably will not get the prop feathered after that. Flying a twin with one stopped in fine pitch is miserable, and you will not get the performance stated by the flight manual (it might not climb at all).