ehat tires are you guys running on 18x7 et 40
wheels

looking for a 40 series tire

 

What suspension are you running?

If you have stock suspension then use 215/40-18, fits rims 7 to 8.5" wide and has tire diameter of 24.8" which is about 0.4" taller than stock but can be used.

If you have lowered suspension you will have less clearance in the rear and might need to adjust suspension with more negative rear camber and trim the inside wheel arch plastic a little with a dremmel tool.

225/40-18 is too tall for the MINI.

If you like runflats then
205/40-18 is suitable and also the Yokohama S.Drive Ultra High Perf Summer tire comes in this size which is same as stock tire diameter for good clearance with stock or lowered suspension.

For your wheels the other common size tire is 215/35-18 and you can find ones that have softer sidewalls for a less stiff ride and more comfort.
For example, General Exclaim UHP would be OK for street use but not really a great handling tire.