Gun fit is everything, and it is difficult to put a price on that. Don't get married to a specific brand- you simply must shoot what fits you the best. This is one area where you may not get what you pay for- I had a Browning superposed lightning from the early sixties- 20 gauge- a "perfect" grouse gun, and I couldn't hit squat with it. It simply didn't fit. I sure did like the IDEA of it, though.
Check out a used Browning Citori. They are well made and hold up to a good deal of abuse. SKB makes a nice O/U, if they fit you. Mine did not. Finally, a used Beretta Onyx or similar grade would be a fine shotgun. Berettas have a bit less drop in the stock, and for that reason fit me better.
If possible push your budget out from $600 to $800, and you will have a lot more to work with. 12 Gauge guns are a dime a dozen, so shop smart. If you have the chance check out www.jaquas.com- Jaquas is in Ohio (I think) and they sell a crapload of shotguns.
if cost is a factor i highly recommend a beretta A390 series automatic. the stocks have an easy effective method for adjusting cant and drop and if you get one that shoots flat* you can use it for sporting clays, and even bird hunting.
*when you shoulder the gun and the 2 beads on the rib line up as one then the gun shoots "flat" or dead on. this is what i prefer. if you see rib between the beads then the gun will shoot high which is what most dedicated trap shooters prefer. for me its more instinctual to cover up the bird as opposed to holding under it.
When I finally bought an O/U it was more the end of a 20+ year wait. Working in trap clubs I could dominate the field with a beretta my boss owned.
I bought a Beretta White Wing, new, and I got it for like $800. Yes I got a deal on it, but I think it was a new model that year. I use it for sporting clays, trap, skeet and hunting. Fun gun. Shortly after that my Bro bought a used O/U for less money that was just as good, or even better than mine. It was a Remington.
I want a few more O/U's but I am sure I will buy them used.
Trap, stand at/from 16 to 27 yards from the box, and shoot single or paired targets on the way out. Read you want a long barreled gun with a steady smooth swing, and since the targets are climbing up, you want a shotgun to shoot 12 to 18 inches above the bead. As for an O/U and doubles, the barrels should be regulated for around 30ish yards (depends where you are breaking the doubles at).
Skeet, stand between two towers and shot targets that at are thrown out, towards, and a crossed from you. With the targets shot correctly, the farthest shot you will make is 23 yards, and the closest shot will be at about 2 yard (Position 8). Read you want a gun that swings fast and will shoot just above the bed, and has barrel regulated for about 13 yards since you will be shooting doubles.
These two sports are world apart, and if a single gun were to be used for both, then at the very least an Auto that you can change barrel would be in order. Also to add, since the POI over the POA is going to differ between the two sports as well, an auto shotgun that allows you to change the comb height would be favorable as well.
My take for a combo shotgun for the two would be something like a 390/ 391 with the following,
26" barrel for skeet, and either a 28" or 30" barrel depending on if you will be shooting doubles or a great deal of time is spent at the back line during handicap.
Both the short butt pad, and the long butt pad should be purchased (they both fit without needed to be fitted). On the trap line, you want the longer LOP to slow the shotgun down, and on the skeet line, the shorter butt pad to decrease the LOP to quicken up the swing.
As for the POI over the POA, the 391 butt stock comb height can be adjusted via the butt stock shim (in between the butt stock and receiver) to change just how high the shotgun will shoot above the bead as your check is welded to the stock.
As for a pump action shotgun in either, it's a tad way too old school, since often when pumping the action, you break your check weld, and the end result is a lose target (more in double trap that skeet). In regards to an O/U able to be set up for both, it’s not going to happen in your budget. And, in regards to an auto, you want a shotgun that will allow you to adjust both comb height, and length of pull at will (read without having to take it to a smith), so choice a model that offers these features instead of just settle for a smith fitting that will just kind of work for the both.
if you got the coin, the Beretta 682 series is your ticket, if not, then a lesser model in their o/u lineup.
Get a sporting clays model 28". 28" is short enough for skeet and it'll do just fine in trap, and sporting clays as well.
A 28" o/u is equivalent to a 25" semiauto because it doesn't need 3" of space for a bolt to deal with a 3" shell.
Get a model that doesnt have an automatic safety that engages everytime you break it open and reload then shut it close. That'll drive you nuts.
O/U's are more durable than semi autos for the untold thousands of rounds a skeet/trap shooter typically shoots. It also means your shells won't eject to the ground and you wont have to spend 10-15 minutes picking them all up after you're done shooting.
Here's my 682 Super Sporting: