I'd like to replace the stock rims on my 2003 S with a smaller diameter set that will let me put tires that'll give a better ride.

I can figure out the wheel and tire diameter to make sure they're similar, but I see some threads talking about 15" rims not working w/ the S brake calipers. I found some OEM 15" rims on craigslist, but don't want to get into a situation of having to grind or replace my calipers.

Any experts in this area?

 

OEM 15 rims and non OEM worked fine....used them as with her rims.
Had a set of both...no issues.
The caveat is you can't have a BBK upgrade, and JCW red calipers or the "poor man's" conversion to gen2 brakes.
But stock r53 calipers are fine, zero issues.
Running 185 width is ok..will depend on the tire...many run this width for winter...there is a combo that gives you the exact same diameter as the 16 OEM rim/tire combo....the r50's 175 is just too narrow.

 

As long as you have the stock brakes, any MINI 15" wheel will fit. The Hollies ( R81 ) are the lightest and most popular for the 15"

Here are all the 15" wheels

https://www.ecstuning.com/Mini-2003-Cooper-R53-S-Coupe-L4_1.6L_W11B16A/Wheels/OEM_Alloys/