The cheapest way to create a racing seat is the way it's done in basically every open wheel series: Take a big plastic bag, fill it with polyurethane foam, sit on it in your driving position (if your body isn't of the superleggera type, hold on to something ), wait until it keeps its shape, stand up, let it harden, cut and decorate as you like -> voilà.
As inspiration for the DIY crowd, I used to run sales for a company called "thunderseat" back in the 1995 and we pretty much pioneered this gaming furniture concept. The best seller was a hollow baja-style offroad chair with a hole in the bottom and an 8" subwoofer bolted to it with an airtight seal. A few years ago while consulting for Razor Scooters, they had the Pyramat line, which is cheesey to say the least. One of our suppliers, Hunsaker Industries, created the "battle chair", and there were half a dozen other imitators including one clamshell device that was too hard to sit on. Another option is to get what was called the "Aura Bass Shaker" an electro magnet system that vibrated. Bolt it to a surface and have an impromptu speaker. We did that to the indy car and boy, that rocked until the friction from poor ventilation damn near cooked a gamer.