what weeds i have are

London rocket
milkweed
crabgrass
and a few others

we do not have a lawn its all rock so killing the grass is not a problem

we do have a few trees and bushes though

Cheapest way is on your hands and knees or add additional plants that butterflies like and call it quits on removing all the weeds. Crabgrass is best handled by a pre-emergent which may be too late in Arizona. The others listed are broad leaf so would need another type of weed killer.