Sounds like the S-spokes
Give the car a go with standard suspension, if you want to improve the looks, try a set of 18" wheels before you change the suspension.
I don't know what your opinion is on road comfort but the standard sport suspension is ideal for the road, if you want to track it it's not great.
The problem is with the suspension on the MINI is that the lowered springs + dampers tend to be track focused meaning they bounce a bit and tend to get tiresome after a while.
That's why i've kept the suspension on mine standard, but then i do have a VX220 for when i want something silly