You might inquire if they have one of Winchester's new lever-action shotguns (They were introduced in 1887, so its close) otherwise you'd most likely be limited to any number of double-barrel shotguns. There are different manufacturers but they're basically the same. A coach gun would be a shotgun with shorter barrels, useful for maneuvering in tight spaces.
A 12 gauge (that's 12 bore in the UK) is the standard size these days, but larger bores were more common in years gone by. Numbers go down in pairs as the bore gets larger (12 is smaller than 10, which is smaller than 8, and so on.) A 4 bore is essentially an elephant gun. For fighting other people a 10 or 12 is plenty, and a 16 or 20 is fully adequate. Smaller bores such as 20 or 28 are also typically considered women's guns, but not exclusively so.
Hope that helps.
(FYI, an easy way to understand the bore sizes is that they are a certain fraction of a pound. I.e., a lead ball the size of a 12 gauge barrel weighs 1/12th of a pound. A lead ball the size of a 4 gauge barrel weighs 1/4 of a pound, and so on.)
