You can mix in some compost if you want. Do not use steer manure. It's too hot for a vegetable garden. A little chicken manure can be good. Steer manure is good for grass.They are clean unused food grade plastic barrels.
I live in Enid, Oklahoma. Is compost/manure needed too?
I can verify on the lumber part of your post. We have 8'x4' boxes built of untreated wood, and we've had these for two years now. Last week we disassembled all of them and moved them to a new location.I'd poke holes in them from drainage. Raised bed soils can dry out quicker so stay ahead of it and mulch well.
I can get 2 yrds of 1/2 top soil and the other 1/2 mushroom compost in my trailer from the nursery a few miles away.
I use untreated(chemical free ) lawn grass clippings and tree leaves mostly.
Worms love it .
My raised beds are good sized from 2x lumber(not treated so they need repair about every 4 yrs).
Some are in recycled cedar which will last long while.
Plan on building 4-6 more this year ..should help keep me busy when I retire next year.