A shotgun setup for a dynamic shotgun fundamentals course, is not likely to be well suited to skeet or trap as well. Usually that type of shotgun has a shorter than average barrel and is setup to be fast and maneuverable for moving and shooting buck shot and/or slugs at various range targets. It is certainly possible to get a shotgun that can sort of do both roles but most "dynamic" shotgun builds will be something like an 18.5" or 14" and have modern furniture, optics, shot cards, slings etc.
In comparison, a shotgun setup for trap/skeet is usually much longer than that (24"+) and you would want different removeable choke options, which matter less to a dynamic shotgun. Trap/skeet guns can also be harder to mount optics on (depending on the model) and they are designed mostly for static shooting at flying objects with birdshot/target loads.
As for capacity, I believe that semi auto shotguns are legally limited to five rounds per mag, but you should verify that info, as I sold all my semi auto shotguns a while back and our laws are constantly changing.
Although, on that note, be aware that in general, semi auto firearms with removable box magazines are definitely on the Gov chopping block lately, so be mindful of that when purchasing.
If you're wanting 10+ capacity, one of the various KSG pump action models might suit you well but it has a dual tube magazine system and it's not semi auto.
Or you could go with a more traditional magazine tube fed pump or semi auto shotgun and put a Canada legal tube extension on it from somewhere like SJ. A Beretta A300UP semi auto with a SJ tube extension would be a pretty solid choice for all around setup for what you're asking imo but keep in mind the limitations of a "do it all setup". The A300 line in general is worth looking into, I think they may have something for what you're asking or at least get you close.
Anyway, that's my .02. I hope it helps some. Best of luck in your quest!
