I rode Big Apples for ten years, wore through three sets of tires. Rotated them and kept going until the casing showed through the tread. Zero flats. None. This is for a guy riding at 180 to 200 pounds on a heavy city bike, always some load in bags. Riding alleys, vacant lots, jumping curbs, riding down stairways, riding ice and snow and just beating up those tires. They do not flat. Only switched tires recently because I figured I could get away with less flat protection.

Flat protection barriers make any tire ride horribly. Most riders who want that feature are just entirely insensitive to comfort or traction. Simplest way to minimize flats is reduce pressure. Stand back and observe bike and rider with static load. The tire should visibly sag at least a little. If pressure is too low steering will be sloppy and you will get another type of flat, snake-bite or pinch flat, which is tube trapped between tire and rim when striking bumps or obstacles.

OEM rim on your bike will be fine with most tires. Bikes are not that demanding. If you have something unusual, like antique 18mm wide tires or 5 inch fat bike tire, yes, find correct rims. The difference between 2.00 and 2.25 tires does not matter.

Big Apples come in different widths. What is available is different for different rim diameters. Mine were all 622-50 (same thing as 700x50 or 29x2.00 and that is another discussion) and with a 19mm internal width rim were 46 to 48mm wide, depending on pressure and wear.

Big Apples ride extraordinarily well for a utility tire. Schwalbe designs for no flats, no flats, and no flats. When that is done they put in other good stuff. The flat free tires they throw out all other considerations. I also ride on Schwalbe tubulars. Out of production. One of them, on a front wheel, has been going for four seasons now and must be close to 10,000 miles. No flats. Tubulars do not do that. Schwalbes do.