Based strictly on those prickly weeds, I looked at those pics and thought, "is that in AZ?" I have some of those in my yard and they are awful!!! And painful!
I would suggest digging them out with a shovel or something. Then to pick them up, use tongs (like the kind from your kitchen). I have a pair of dedicated cactus tongs I use for things too prickly to touch.
Mesquite trees are nice, low water use and grow super fast. You can buy the 5 gal size at Lowe's for about $18.
re: dog poop, I have to say that the best 20 bucks I ever spent was on a pooper scooper.