I've owned numerous (too many, really ! ) shotguns over the past 45 years, including O/U's, SxS's, semis, pumps and even a couple of single barrel trap guns. Tried the multi-barrel approach with Mod 12's & 870's, 58's, 1100's and SX-1's.
Looking back, the closest I could come in recommending a "do-it-all" target gun would be either a Browning or Beretta 30" Sporter ...with interchangeable choke tubes and an adjustable comb. New is admittedy somewhat expensive, but I see no problem with say a Browning 425, 525 or 625 or a Beretta 682 Sporter that's been used and well-cared for.
As a close second, in a semi, a Beretta 391 or A400 with 28" barrel.
I've had no problems shooting all the target games with 30" O/U's, including International Trap & Skeet. American Skeet seems best with 28" or 30" and most ATA Trap shooters seem to prefer either a 30" or 32". The rage in Sporters for the past several years seems to be 32" (I have a 32" DT-10 that has worked nicely for me for the past dozen years, and previously had a couple of 32" Brownings) but some adjustment is required to be effective with the longer barrels for Skeet.
Of all the semi's I've owned, a Beretta 391 "Parallel Target" is the one I've been most successful with. I have two barrels for it, a 28" and a 30". Seems I have the 28" barrel on it more than the 30" ... just seems to balance and swing better. I much prefer the Parallel stocked version ... it has a relatively "flat" comb and different grip radius as well as a stepped rib. Just suits me better than the standard version sporting configuration.
Other than choke selection, no big difference is noticeable between a pure "Skeet" gun and a "Sporter", although many Skeet shooter prefer a heavier gun. Both are relatively flat shooting, and both should be balanced about the same. When shooting Skeet with a pre-mounted gun, a slightly higher comb than a gun-down Sporter can be used.To switch over to Trap, most want a higher shooting gun ... somethin that patterns 70/30 or better. Simply raise your adjustable comb a bit (after patterning to determine "how much") and don't be worried by seeing a bit of rib.
Works for me !