Depends on the angle you shoot at. and shot size.

If it's a pigeon or other bird in flight and you're shooting upward then the safety distance will be longer. If it's on the ground at a rabbit or fox, etc. then the ground will absorb the impact and the safety distance can be shortened.

The distance the shot will carry, as said above, depends on the shot size. Birdshot, etc may go a couple of hundred yards given the right elevation/angle of shooting. Other projectiles like a slug, etc will go further.

The easiest way is to make sure you know what behind your target or in the distance. Then pick your shot accordingly.

At 300 mtrs, with a half choke and say 32gr 6/5 or something similar i would consider that more than adequate.

While we have to be careful i would say this, and it's not meant to be ignorant of the dangers, but if you over think every shot then chances are you'll pause/hesitate on some shots when it's not necessary. Many years ago i was out on the border of the gun club lands. It borders another club. There is a small lake, and heavy, heavy, bush/tree coverage. Someone from the other club fired a shot. Now the shot seemed to be a bit away (at a guess around 200 yards). The shot fell around me. Now while i heard it and some did hit me/around me i was not injured and did not get hurt.

As he could not see me, and it was not a good idea to hang around i left, fairly sharpish. I don't know what shot, gun, or choke he was using so cannot say this was a safe distance or just "dumb luck". However when you consider that the maximum effective range of a shotgun shot with the average cartridge/load and choke combo is between 40 to 65 yards if you treble that it's less than 200 yards and seems more than safe.

Lastly you must consider the spread of the shot itself. The average 32 gr 6 shot has about 250 or so (maybe less) pellets in it. With a half or 3/4 choke you are looking at an effective range of about 45 yards or so. Perhaps a little more. However the further the shot travels the more it spreads (as you know). So if you place a target (cardboard) at a distance of 100, 150, and 200 yards and fired at such an angle so as to hit it you might find that few shots actually hit the target, and i'd be surprised if any actually penetrated the target at the longer distances.

Obviously the heavier load, and tighter cartridge will elongate this effective and maximum range, but i'd still be hard pushed to think a shotgun shot (any type used for hunting here) could do harm or serious harm at such distances. Due to spread of the shot and the velocity of the shot at the distances you are talking about.