First off, welcome to the forum.
33" is the largest you are going to be able to fit without a lift. However, if you go off road much, you will probably get some rubbing on the fenders. But on road everyday driving shouldn't be an issue.
Now, everything above is contingent on the backspacing of the wheel and/or the width of the tire. If you throw some 305/65/17s (essentially a 33x12 tire) on the stock wheels, you are going to get lots of rubbing on your front airdam and most likely your rear swaybar end links as well. However, if you added 1.5" wheels spacers, you would lessen this chance. With wheel spacers and something like a 285/70/17 (basically a 33x11), you should be fine.
Of course, you could forgo the wheel spacers and just get new wheels with appropriate backspacing. Something in the 4.5" and under range is desired.
Now, if you want to get a 33" tire on your stock wheels but don't want to use wheel spacers, then you need to look into something like the 255/80/17 BFG KM2. That is a tall and skinny tire (33x10) and has been known to fit with no rubbing whatsoever.
Now, as for your question on smaller rims and bigger tires.........
There are several 15" wheels you can fit on your JK without fear of rubbing the caliper. Examples would be Level 8 Trackers (3.33" of backspace), MB72s (3.75" of backspace), Black Rock 909s (4" of backspace), etc. However there are also many 15" wheels that will not work without some grinding down of the caliper.
Reason I bring up the 15" wheels is because, in many cases, you can score brand new 15" wheels AND tires for less than the price of just tires for 17"+ wheels.
As you could see by my examples, most of the 15" wheels have backspacing in the 4" and under range. If this is going to cause the wheel/tire to stick out too much for your liking, you can look into 16" wheels, which more often has 4.5" or so of backspacing. This will keep the wheel/tire slightly more tucked under the fender the 15s.