To run these in an 18x7.5 with the 2.5inch lip? Or the 17x9 with the 2.5inch lip? Also going to be running m7 springs

 

http://www.sportmaxwheel.com/sportmax_006.shtml

 

?

 

To determine fitment you need to-

Choose a wheel with-
Bolt pattern 4x100
Offset of about +42 to +48mm
Has a width up to about 8", any wider and offset becomes less like +30mm but then the tire sticks out wide out of the wheel well and if the tire is tall it will rub the wheel arch liner. If offset is too much like +48mm then you risk hitting the rear trailing arm or suspension parts in the rear.

Choose a tire that fits the rim selected and
has a outer tire diameter of 24.4" or less. 24" is pretty safe for a lowered car.

You cannot put any rim on a MINI.
For the link you mentioned no bolt pattern was specified other than 4 lug which doesn't specify 4x100 or 4x114 both of which are common.

Also offsets are not mentioned which are crucial.

At http://www.wheelmax.com/wheelFitTocar.asp
For a 2006 MCS
Sport Max 006 Black with chrome lip
17x7 4x100 +40mm offset $156.44 each
18x7.5 4x100 +42mm offset $177.44 each

I'd say that in this case both rims would work with the right sized tires.
You want enough clearance for the M7 springs which are moderately lowered.

For 17" tires look at 215/40-17 for best clearance. 205/45-17 would also work. For 18" tires look for 215/35-18 or 225/35-18.