To each his own
10 boxes a month seems to be pretty reasonable. The Browning Gold will do what you want it to, as long as it fits you and you take the time to get to know the gun's mount, aim point, and break point.
You've gotten some pretty good advice so far, on O/U's, autos and pumps. For skeet, a lot depends on the club where you shoot, and whether you choose to reload shells or not. If you reload and want to keep your hulls, some clubs' rules mandate that if a shell hits the ground, it belongs to the club. This makes pumps and autos a problem on skeet, because it's tough to shoot skeet with a shell catcher (not impossible, but tough). As a result, the O/U is probably the way to go. If you don't reload and don't mind losing the hulls--shoot whatever you want. You're there to have fun, right?
I shoot trap (for now) with a pump, although I've used doubles and an autoloader. For reliability, consider that Vic Reinders put over 608,000 rounds through a Remington Model 31 pump (and Reinders was repeat national champion). Any shotgun can require parts, repairs, or extra attention over time, but this old story is why I shoot two 31's: One with a poly-choke on Modified, and one with a Cutts with a Full tube. I get a lot of chuckles and elbow-digging and smart remarks from the four-figure gun crowd when I uncase the old howitzer-nose, but they get awfully nervous when I shoot the same 22 or 23 that they did. The guy at my club who shoots 25's routinely is nice and says "nice shooting!" regardless of what you carry.
Neither model 31 cost me more than $250 used. If I had decided to stop at one, I could have had $250 to buy shot ($50), powder ($20), primers ($40), wads ($10) and 15 boxes of nice, Winchester AA trap loads at $8 a box.
Get what fits you, and get what will bring you joy, and you'll rarely regret the decision.