In many ways, the choices were very similar to what is appearing on the menus of hotels and family dining locations today.  Here is an example from the 1912 book The Potato by EH Grubb & WS Guilford of the famous Brown Palace Hotel in Denver Colorado:

Potatoes, French Fried		15
Potatoes, Saratoga Chips		20
Potatoes, O’Brien		30
Potatoes, Hashed Brown		20
Potatoes, Au Gratin		25
Potatoes, German Fried		20
Potatoes, Baked		15
Potatoes, Julienne		25
Potatoes, Sauté		15
Potatoes, Parisienne		15
Potatoes, Lyonnaise		20
Potatoes, stewed in cream		25

By the way, those prices are in cents and not dollars.One of the most famous restaurants’ recipes for potatoes comes from Delmonico’s of New York…Potatoes Anna.  The procedure was to cut very thin slices from across the largest potatoes, lay the slices in flat layers on a small plate, spread butter freely (I like that term) over the potatoes, then add another layer, and so on until the potatoes are about four inches high. Bake until the potatoes are tender (about one half hour) in a quick oven…note, no temperature given, but I would start at 350-375° F.  Here is some history on the restaurant, which originally opened in 1837. The restaurant has re-opened and now you can find potato side dishes for 8-12 dollars, not cents.