I'll make some corrections. It seems most cars are obtainable in Story Mode. The Mitsubishi Eclipse GSX can be used early on, and with customization, it can reach speeds of over 233mph. Don't forget to upgrade your garage. If you find progression difficult, consider acquiring the Koenigsegg Regera. There are plenty of other cars available to dominate the Grand.
Note: You can replay the previous day multiple times if you don't clear the weekend races. It's easier to progress by choosing higher-stakes races. There are methods to earn money by escaping Heat 5 police when you're short on cash. If you feel like you're about to get caught, exiting the game and restarting will retain your money without the pursuit continuing.
