Honestly, I was in a similar position about 8 years ago when I was your age and just getting into shooting. My budget was the same. Originally, I had plans for a $2000 Beretta O/U. I found some Beretta 3901 20 gauge with ugly grey synthetic stock on clearance at a local gun shop for $550 and decided to get that instead. I am really glad I did as it has been an awesome gun. This version of the 3901 was made in Italy (most of the less expensive ones were made in the US with Turkish barrels). Since getting it, I have shot tons of skeet, taken it small game hunting, deer hunting, turkey hunting and more recently quail and upland bird hunting. It is very versatile.
For you, I would look at a used 1100 in a left hand model. A quick search on GunBroker
finds a couple well within your price range. That leaves money for another barrel, or to have it refinished (since one in your price range may have some use on it). I'd also start with a 12 gauge and shoot light target loads. The light target loads will be about the same as a normal 20 gauge, but they will feel lighter in the larger, heavier gun.
If you are serious about skeet, then I would not recommend a pump action. You'll have enough things to think about without trying to work that into your game.
Also, a target/field shotgun isn't exactly like our Tacomas. I would not suggest making any serious 'mods' to it. I would recommend getting it fit and spending any left over money on lessons or more shells. Definitely don't go get an 870 and put a tacticool stock on it and then bring it to the skeet fields.