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 - Ohlins TTX, Fall-Line Suspension Arms/Bushings, AP Racing BBK, OE GTS Aero, Cobra Seats, Akrapovic GT4, GMG 4-point, BBS E88