This is actually a thing people are doing: no processed foods for a month. I already sort of follow that diet, trying my best to follow the "if your great-grandma wouldn't know what it is, don't eat it" rule, aka "if it is a plant, yes; if it was made in a plant, no" rule, aka the "can you make it in your own kitchen?" test. There's really nothing to lose by trying it out (besides probably a few pounds, unprocessed is undoubtedly healthier).
By these guidelines, fruits, veggies, pasta, bread, cheese, milk, meats, nuts, & even many sweets are fair game--provided these things don't have additives, preservatives, or other chemical fillers (think bread that also has high fructose corn syrup). Things like cake, cookies, & alcohol are fine, provided it's in moderation and preferably homemade.
The creator of this challenge usually allows for things you could make in your own kitchen, but for reasons of time and convenience usually don't: coffee, cheese, chocolate, pasta, etc. Then what it comes down to is checking ingredient lists and packaging. As a rule, the less packaging the better (think purchasing fruit vs fruit roll ups). Frozen fruits & veggies are better than canned when fresh isn't available and grass fed/sustainable/organic meats trump their corn fed/factory farmed counterparts. When grocery shopping, stick to the outside aisles, where most of the unprocessed food resides, and avoid all the canned, boxed, and chemical-laden inside aisles.
Don't go for the month right away if it intimidates you--but try going unprocessed for a week, or even one day a week. I promise it's actually quite easy once you've tried!