I am in Ohio also. I have never kept pygmies and I have always had Alpines. Goats usually have a pecking order, so I would anticipate that a larger goat would, at least, initially "put them in their place." Also, when you feed them hay or grain, I would anticipate that they would need a separate feeders, if not area.
The biggest difference would be the milking routine....and you will need a milk stand, stainless steel bucket for milking, a strainer, filters for the strainer, additional grain while they are milking, a pasteurizer (unless you are planning to drink raw milk), a mineral/vitamin supplement, routine worming, and vaccinations.
You need a plan for getting her bred.....a buck nearby.....and a buck "jar" is, in my opinion, the most practical approach for 1 or 2 does.
And you will probably need a separate pen for the babies that she will have when she freshens.....and bottles, nipples, etc. to btlle feed the babies....and a plan to disbud the babies (for 1 or 2 does, the vet or a goat breeder who may be willing to do it for you is probably the most practical approach).
Pick up a book on goats at Tractor Supply......I think they carry the Storey book.
Goats are addictive.....I bet you can't have just one milker.
Good Luck!!!