[Helix_FR]

28 gauge is smaller than the 20 gauge but bigger than the 410. The sizes go like this. 10ga, 12ga, 16ga, 20ga, 28ga and 410. I've been seeing a large influx of 28 ga recently but used guns in 28ga bring a premium bc they were way more rare until a few years ago. Yes what I have pictured is considered a over/under or what browning calls "superposed". That particular one is the CZ Woodcock series but they start at about 1000.00 but I have seen as low as 800.00
500.00 for a double is modest. You may be better finding used than new at that cost. New For 500 mossberg makes a nice entry O/U called the silver reserve. Used I encourage looking at Stoeger Condors, Ithaca 500's, Savage golds, SKB's and even CZ has some used ones I've seen in the 500.00 range.
Most importantly as others have said, make sure when you put it to your shoulder you don't need to reach, meaning you need to stretch your arms out to get it over to your shoulder. That would indicate that its too long. Put the gun to your shoulder like your going to shoot it. drop your trigger hand off the gun, does it stay balanced? or does it want to fall forward using your other hand as a pivot. If it falls forward easily then the overall length is too long for your fore arm hand, this would make the gun hard to swing in skeet shooting. Find one that fits? bring it up and aim with it. Does your dominant eye fall right down the rib of the barrel or do you need to smash your face into the stock to get your eye low enough? This would be the comb is too high. If you need to lift your head, then the comb is too low. Low comb can easily be fixed with a comb pad which are easy to find.

I almost forgot. The shells get ejected when you open the barrels after shooting them. Press the release lever and the gun will open at the barrels and the ejectors will kick the old shells out, just aim over your sholder, they will kick into your face if ya hold it that way. If you don,t shoot the shells and open the action the ejectors will nicely push them out for you to grab and not chuck them over your shoulder.

The pump gun is up to you. Pumps are generally lighter in weight and more common. 500 for a pump is easy but there are some real pieces of junk out there too that were abused buy previous owners. Many people abuse pump guns but not so much with doubles.