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.
'13 SSII M3 Coupe - KW Clubsport 3-way, Akrapovic Evolution, ESS Tune, StopTech Trophy, IND Euro Front Bumper and Gloss Black Mirror Covers, TMS Studs/Lugs, BMW Performance Carbon Fiber Spoiler/Interior Trim/Center Console, BMW Edition Grills/Gills, BMWPedals Extended DCT Paddles, Mode Carbon GT4 Splitter, Advan TC3, BBS E05