It does not matter on tread pattern. Any tread pattern of same size will work as spare.
If you change sizes, one size up (275 series) should still be fine to work with stock 265 series spare. The difference between a worn tire and a new tire is about the same difference as a new 265 to a new 275.
Now going to a 285 series tires, it's up to you. The difference in diameters will be slightly more than the difference between worn and new, so use caution. I would get a matching size spare if I were going to use a 285 size, but that's me. Also a 285 series will still fit in your original spare tire location. Any bigger and it will not fit.
Going up to 295-305 I definitely recommend getting a spare to match these tires. Hope this helps.
If it were me, I'd run the full size spare if you do anything more than just light 4-wheeling. It sucks to be out on the trail, get a flat, then try and limp out with one small tire. If you just drive on the street, I'd stick with the smaller spare. That being said, you could probably get a used tire and have it mounted/balanced for under 50 bucks.