So I have decided on the wheels I want, but now I am torn between going with the 17's or 18's. I am pretty sure I want to go with the 18x7.5's with a set of 225/40's on them. First off, will this 18" wheel/tire combo fit without rubbing? Second, will I be able to lower it with this combo if I decided to later? I guess my other option would be 17x7's with a set of 215/45's on them.

I am pretty much only concerned with looks as this is my daily driver. So I just want what ever is going to look/fit the best. Anyone have any exerience here?

Oh, and these are the wheels I have just fallen in love with.

 

225/40-18 is not a good choice for the MINI no matter what wheels you get.
Tire diameter is too all at 25.1" and won't work for any lowered suspension.

18x7.5 could work, what offset will you use? +42 to +45mm offset could work. Use a tire with less than stock tire diameter or about 24.1" or less.

225/35-18 would be a good choice. Fits rims 7.5-9" wide. Tire diameter of 24.2". Good tire would be Goodyear Eagle F1 Asymmetric for best handling.
If you want good tread appearance and can put up with a bit more noise then Yokohama Parada Spec-2 and BF Goodrich g-Force T/A KDW2 are nice looking.

For better value and street comfort-
Yokohama S.Drive Ultra High Perf Summer tires 300 treadwear $137 each

In 215/35-18
Another good value and good comfortable street tire is-
General Exclaim UHP Ultra High Perf Summer tire 380 treadwear $93 each
23.9" tire diameter is small so more clearance for lowered suspension but more wheel gap than stock. This tire also comes in 215/40-18 which is a little taller than stock- OK for stock suspension but a bit tall for lowered suspension- still possible.

If you have bad rough roads think about damage to rims and suspension if you have lower profile tires like 35 series sidewalls.

 

they only come in a +45