I would budget more like a grand, minimum. A few hundred in gasoline, two or three hundred in tire wear (depends entirely on the cost of the tires, obv), brake wear, etc. Not to mention the potential of physical damage that won't be covered by regular insurance, so if you want to buy track insurance that will be a couple hundred more.
I do love taking my car out to the track, but my wallet feels it every time.
It's $400 for a HPDE day at my local track, and it's done on a weekday so I gotta take the day off of work.
Racing on the streets is free.