I really like the style of this home and have been trying to find some plans online of similarly styled homes. What exactly should I be looking for?
I would call it a contemporary ranch.
It might be considered Contemporary/Ranch but it has far too much of a Neo-Eclectic character. It might be considered Neo-Mediterranean or Neo-French (Colonial) but the traditional features have been greatly simplified.
Location, year of construction and interior features would be a big help but from the photo it is not typical of any style.
The home was built in the late 1960's in Houston, TX.
I really like the roof, the long front porch, and the brick columns. 40-50 years later, the home doesn't look outdated.
I don't think you could easily put a label on that style because it's not your cookie cutter anything. In fact, I'd suspect that it once was a rather typical ranch that has been extensively updated fairly recently. (77024?)
If you're plan-shopping, I'd search for a 'ranch' or 'transitional' style, find a floor plan you like, then show this picture to an architect for modifications to your 'boxed' plan.