I would stick with 19's. Since that is the case.... LM's are your best option. LMR's are not available in anything wider than 10" in 19's. That's too narrow. I would get LM's in 19x9.5 front, 19x11 rear.
'04 E46 M3 - Jet Black - Sold
'08 E90 M3 - Alpine White - Sold
'13 E92 M3 - Silverstone II - Sold
'13 E92 M3 - Alpine White - 1 Option (DCT), Ohlins TTX, AP Racing, Cobra Seats, Akrapovic GT4, BBS E88, Volk TE37, M3 GTS - Steering Wheel, Aero, 1/2 Cage, Seat Delete