I personally highly recommend a Beretta 68x over/under. Yes, it will be more than your $1,500 budget (well, might find something used that's close) but it will last you a life time...literally. They are the Timex watches of O/U shotguns.
Now, many do indeed like Brownings. For me, Brownings sit too high in the hand and I find the Beretta's to be more pointable (we point a shotgun, right...we don't aim them).
As for gun fit...as a former registered skeet shooter (yeah, I competed for a very long time...which is NOT to say I was ever competitive! haha) I believe that I have a great deal of shotgun fitting experience and many adjustable features for fit that rifle chassis/stock makers are incorporating in recent years were extremely common on clay target guns for decades.
IMO, unless you are the one person that Beretta (or fill in the brand name blank) made their stock fit then you need to make it fit.
LOP can be adjusted by cutting the stock or using shorter/longer recoil pads.
Adjustable combs for both up/down and left/right are pretty much required for proper fit.
Also, many (including me) prefer a parallel comb vs the traditional drop at heel. A parallel comb (parallel to the bore) means that no matter where I put my face on the comb, my eye will be in the right place relative to the rib. Also, the comb won't be driven into my face on recoil. When shooting 400 targets in a skeet tournament (or 500 if you shoot doubles), comfort and reducing the effect of recoil gets to be pretty important.
Adjustable butt pads....and particularly the ability to cant the toe outward...are not necessarily universal but are very common on skeet and trap guns and less so on sporting clay guns. Since we shoot shotguns offhand, and most men have a groove between their pectoral and their shoulder that slants down and out, kicking the toe out lets the pad fit your shoulder pocket properly while keeping the shotgun level to gravity. For woman, an adjustable pad let's them get the pad off their breast.
Also with adjustable pads...for high gun games like skeet and trap...many people will find that lowering the pad is very helpful. We want the pad in our shoulder pocket and dropping the pad a bit brings the gun up to the face without having to crawl the stock. Pad adjustment to get the gun up (and therefore head is upright) and the comb vertical adjustment defines the relationship of the on eye (which is the rear sight) to the comb and this determines where the gun shoots in the vertical.
Finally, pitch...which is the angle of the pad if you looked at it from the side. You want the pad to press evenly across your the contact area of your body and do NOT want the heel or the toe digging in both for comfort and to eliminate gun flip on recoil.
So, like I tried to say...yeah, gun fit is VERY important in a shotgun but factory stocks do NOT properly fit most people and theses adjustable featres are the tried and true approach (aside from spending big $$ on a custom stock) to resolve this.
For low gun...sporting clays and in particular upland bird hunting, I'd just put an adjustable comb on it and leave it as its actually pretty different than pre-mounted clay games.
@DownhillFromHere - you were a much better skeet shooter than I...anything to correct or add?
