The stock tire size for the 16" wheel is 195/55/16.

You can go 17 inch size perfect comfortably. Thats what i ran for over 9 years. Where you need to be careful is with going any larger and whether you are using run flats or not. R53s have an issue with strut top mushrooming/deforming - the larger the wheel, the stiffer the side walls, the more energy is transferred to the strut tops and causing the deforming. Stock minis equipped with the sports package (including the 17 in stock wheels) were  facing these issues. As result i would stay away from anything larger than 17 inch and stick with non-run flats. 

Thanks, whats a good size tire for a 16”  wheel? 

If you stay with the stock sized 16" or 17" wheels with the stock offset and stock tire size, you shouldn't have any problems with rubbing.

Hey yall. i have an r53 and i am looking to wheel/tire and upgrade to coilovers. I am wondering what the Best size wheel and tire I can use without cutting or modifying the fenders or body. I may also be looking to lower it in the near future so any recommendations help!  The wheels I am getting our rota grid v’s.  I am mainly looking for something that looks good and will perform but I absolutely do not want to cut the fenders or anything like that.