I have always heard that style called farm house. Good luck with your project. Please keep the homes character.

Vernacular. Four square is a form not a style- four rooms per floor in a roughly square shape- hence Foursquare. Foursquares can get finished in lots of different styles. Your house regardless of form is broadly traditional American vernacular- it has some colonial revival bits, some late Victorian massing, etc. Generally these were well built houses, replace plumbing and electrical but leave the architecture alone.

I have to agree that this is very much as Hallett describes and IMO you do not have to keep the style on the inside but yes to upgrading all the guts before doing anything else. These houses look great painted like this.So go crazy or much more subdued they both work. Have an awesome time doing this it is very rewarding .

The massing and some of the detailing makes my think Eastlake Victorian style. It is a gorgeous old home and kudos to you for taking it on as a restoration/renovation!