What's wrong with turkey, fish, beef, pork, or eggs? Potatoes, sweet potatoes, yams, oatmeal, or fruit? Tons of guys drop fat while eating any of those foods. Nothing wrong with simplifying the approach, but it's crazy to limit yourself to just three foods for any extended period of time.
Nate Miyaki's paleo-hybrid approach is a pretty straight-forward way of eating. The meals would be simple: A serving of cooked animal, serving of cooked carb source (from appropriate source), serving or raw or cooked vegetables - several times per day.
With that kind of approach, the macros and calories sort themselves out to an extent. You'd adjust things weekly based on the progress you were or weren't seeing.
For fat loss, diet will obviously do a bunch of the work, but your training is definitely a factor too. The best bet is to pick a well-designed routine from the archives and just follow it as-is. Or did you have something in mind already?