The “New” way to start a garden is to use the method taught by Charles Dowding on Youtube.
Cover your grass/area with cardboard and then add 4″ of compost on top.
Make sure the compost is cooled down and then you can plant directly into the compost.
While you can use wood to create a raised bed, it is not necessary.
I usually buy compost locally from https://www.stlcompost.com/compost
Using their calculator, a 4′ x 8′ garden takes about 1/2 cubic yard of compost.
If you either have a pickup truck or have a friend with a pickup truck you can buy the compost for as little as $30/cu. yard.