I don't think there's a particular architectural "style." It looks like it might be a tri-level type of floor plan. Style-wise I think it's plain enough that it could take on a variety of influences. Are you planning an exterior project?

Yep some homes don't have a style. You have a tri level or aka as a side split.

With new paint colors, this could be real attractive. The white does not enhance it.

While the roof of this house is more red than your's, notice how well the earth tones of the trim and body compliments it.

We bought the house in 2016 (as a pre-foreclosure, so it was in really bad shape) and we are finally able to start looking to update the exterior. But I wanted to be sure when we pick colors and deal with the shutters that I keep the style of the home in mind. As far as I can tell the house exterior has not been updated since it was originally built in 1967.

The relatively shallow roof pitches and relatively large roof overhangs, as well as the combo gable/hipped roof on the second level all have a vaguely Asian feel and style to them. It may be possible to enhance that through color or material changes as some of the other commenters have mentioned...

These houses were mass produced from the 50s on because of suburban sprawling. You are not going to ruin the style because it has none.

It's wonderful that you want to be mindful of the home's style. We had a 1968 trilevel in a neighborhood full of late sixties split levels/ tri-levels. One neighbor added victorian accessories including an ornate lamp post that looked very out of place.

Definitely remove the shutters. This house could have a mid-century modern, craftsman or prairie vibe with a few changes and a new color scheme.

Here is a Prairie style home with a low slung roof and plain rectangle windows.

I can see that there is clapboard siding on the second floor, but it is not clear what is on the first story. Is it stucco, board and batten or more clapboard?

more clapboard. Old chipping white that's seen a few decades with dull dirt brown trim. this is the listing photo from 2016, but we hvent done much to spruce the house up externally. Focused on inside livability and did minimal landscaping to manage weeds.

The brown roof is going to probably be your most significant constraint when choosing exterior paint. If the roof needs replacement, black/charcoal gray will be easier to work with.

we are 2-5 years away from replacing the roof and I planned on doing a dark color, so we will paint for the new roof, not the old one.