Based on my gaming experience since day 1. These are just my opinions, please respond if you found better cars to use per class and tell us why and how you do it. Thank you.
Race: Koenigsegg Regera or Porsche 911 Carrera RSR 2.8 (Depending on track terrain, your handling skills and preference).
Drift: Lamborghini Huracan (Most used and produce top high scores) or Mazda RX-7 (Long time real life and Need For Speed Drift Legend).
Drag: Volkswagen Beetle (With wheelie bars for better handling or without it to do wheelie side-bets and fastest 1/4 mile clocked so far) or Beck Kustoms F132.
Offroad: Porsche 911 Carrera RSR 2.8, Chevrolet Bel-Air, Porsche Panamera Turbo or Mitsubishi Lancer Evolution IX (Depending on RWD or AWD preference and Live Tune).
Runner: BMW M5 (House and Police pursuer wrecking machine), Ford Mustang GT (Sport car type), BMW M4 GTS (Drifty), Porsche Panamera Turbo (Sedan car type) or Mitsubishi Lancer Evolution IX (Import sedan car type) (Depending on preferred car type (Sport or sedan cars), Live Tune settings (Strong or lightweight chassis reinforcement) and drifty or stable run).
Performance installed: I preferred 3x Chidori and 3x Outlaw with Acceleration, speed, brakes and nitrous perks on all my car classes. I personally disregard the jump perk unless I need an offroad car to tackle jumps, destroy billboards, collect derelict parts or get chips.
