If you don't currently own a 2017 car they are on sale at the moment. Here is the basic list that I found just going through the cars that can be purchased and the current purchase value. I designate which require the Car Pack/Pass/DLC. Any without a designation are available in the base game:
Acura NSX (Car Pass/DLC) - 119,000 (down from 170,000)
Ford GT - 280,000 (down from 400,000)
Ford Focus RS - 30,100 (down from 43,000)
Ford F-150 Raptor - 44,100 (down from 63,000)
Ford F-150 Raptor Race Truck - 44,100 (down from 63,000)
Jaguar F-Pace S (Car Pass/DLC) - 38,500 (down from 55,000)
Mercedes-AMG GT R (Car Pass/DLC) - 140,000 (down from 200,000)
Nissan GT-R - 92,400 (down from 132,000)
I personally used the Ford GT that I had won in a wheelspin. The cheapest of all of them is the Ford Focus RS, although I would recommend the Nissan GT-R as it seems to be be the highest rated car for the best price (assuming you don't have the Car Pass). You do not need to win the race, just complete it.
Any online race will work. The video below designates a tried and true area - the Drag Race at the Parking Garage in Redstone Airport, and from fast travel from Horizon Festival to race completion took me about 4-5 minutes. Any online race should work, though. Because I accomplished it this way I am not sure if private races will work, please mention in the comments if you find otherwise.