Are you planning to lower suspension or use OEM? This determines your clearance and requirements for wheel offset.

As long as the 15" wheel you choose can fit over the front brake calipers then it should be OK. Since you have 15" wheels I assume you have a base Cooper not Cooper S (has larger front brakes).

While there is nothing wrong with OEM 15" wheels and 175/65-15 all season tires you do have options. Why do you think you need 15x8" wheels? For looks? Why do you need a wide tire size? One problem with the sweet spot for MINI wheels is about 7" wide, 8" is OK but tire sizes that fit the MINI tire diameter aren't as available. This means as you look for tire sizes beyond 205 or 215 mm wide in 15" wheels they might not work as well with any dropped suspension. Go to tirerack and look at which tires you would use then check sizes in 15". Some tire models don't come in any smaller than 17" sizes. You'll find better tire selection in All Season tire classes than in summer tires for 15" wheels.

I have an MCS modded for driving school, track, autocross, etc and use OEM 15x5.5" wheels for daily driving and 195/60-15 all season tires for street use. Still allows for some performance, smoother ride, less noise, longer tread life, lower cost, less rolling resistance and better mpg. I could easily daily drive with Extreme Summer tires in either 16" or 17" wheel and tire sizes but ride quality and comfort would suffer and tires wear fast.

What are you using your MINI primarily for? How many miles per year, any cold weather (assuming you don't use snow tires in winter)?

I also race on 15x8" et36 rims and can mount 225 to 240mm wide tire sizes on them with 1" drop in suspension but these tires are not for street use. I have 200 whp on dyno so I can use wider wheels and tires but with your base cooper and half that power it's not the same experience.

 

I run 15X8 with 35 offset but had to use a spacer to clear the rear trailing arm.

15X8 +20 fits w/o spacer but pokes.

 

Is that with an R56 and did you use longer wheel bolts or change to longer wheel studs? Usually the front wheel can fit without needing spacers but the offset will decide how far the wheel sticks out (pokes). In front with offset of 35-36mm the new wheel will be about 6mm closer to the inner suspension and poke out 32mm more than OEM. If you were to use 20mm offset in front you will poke 47mm or almost 2". If you add wide tires to the 15x8" the tread shoulders will bulge out even more. If you stretch fit a narrow tire you can tuck in the tire but it won't fit on the wide wheel and perform and wear differently than how it was designed (for the OP).

Anytime you can use no spacers by choosing the right wheel offset, it's better but when using spacers you may need longer wheel bolts or studs, otherwise the OEM ones are too short and you have too little threads to lock the wheel securely.

 

OP, if you are considering 15x8" wheels you have to look first at tire models and sizes that will fit the MINI. Look for tire diameter closer to OEM 24.3" if you care about speedo and odometer error and road clearance to clear debris and parking bump stops and speedbumps.

You can choose sizes in the 205 and 215mm wide range but they are generally too narrow for an 8" wide rim. 225/45-15 is a common size for track and autocross use as this fits rims 7-8.5" wide, perfect for 7.5" wide rim so it is usable. Track and autocross tires with treadwear 100-200 won't wear as well for daily street use but if you drive fewer than 5000 miles each year it's possible. Track and autocross tires ride firmly, are noisy and generally don't grip well except when dry and warmer. Tire rubber is hard in cold and there can be little tread grooves for resisting hydroplaning in wet.

225/50-25 and 235/50-15 are possible wider tire sizes that are close to OEM tire diameter but tire selection is more for racing and very limited street use, with OEM suspension there is clearance but with lowered suspension it may be risky for rubbing.

 

Unfortunately it's hard to find the exact right fitment needed. I believe the best offset is a 25-30. 28 is probably ideal for less poke but inner clearance too.

Tire rack lugs are marginally longer. Being that I only run a 1/4" spacer and will move down to a 5MM spacer, I didn't use extended lugs.