I have zero personal experience, but from talking to people who have done it:

I think a safe bet would be $5000/yr to club race on a shoe-string, not including the initial investment in a car and equipment.

$10k/yr minimum to do it right.

$20k/yr minimum to be truly competitive at it.

You have to figure it's going to cost you about $1000 per race weekend. Entry fees... tires... race car, trailer and tow vehicle maintenance and repairs... travel expenses.

It takes a good chunk of disposable income.

As far as time, that depends on how much money you have. If you have more money, you can farm out more of your car prep work and invest less of your own time. You could even rent something like a spec Miata for each race you do... and it might even be cheaper than owning/maintaining your own car.

If you're going to do all of the work yourself, it can take a LOT of your time.