I have an 870 among other SG's, and never put 3" shells through any of them. Regular 2 3/4" 00 buck through the 870 for HD. 2 3/4 field loads for pheasant (through a Benelli SuperNova - yes, collecting SG's can become an issue!). Also have a Browning Citori for skeet and sporties and reload 1200 fps 7/8 oz loads for clay games (a MEC 9000 reloader has made that more affordable). A limbsaver recoil pad (pre-fit, grind to fit or slip on) can make a big difference. No need to get beat up more than necessary.
A Browning BPS is a very well made shotgun that would serve you well in trap. A semi auto or over/under is a better choice for skeet or sporting clays as you need two quick shots sometimes (doubles in skeet for instance) and having to shuck a pump can put you at a bit of a disadvantage. Also, never overlook a used shotgun for any of these disciplines. It would be very difficult to wear out a BPS, 590, Citori, 870, etc.