I personally love the cheapies from Big W and Strandbags.
Right now I have a large, but very light, Leopard print bowlers bag for shopping (ie throwing in the trolley-it has a great swing leverage and a heshion backpack (yes, my spelling is totes shockers today!!) for when we go to parks, the beach, outdoory places and get dirty or bring things home.
I never spend more than $20 usually, and both of them cost me $15 each.
I'm a complete sucker for no pockets though, which won't be any help to you. I obviously just LOVE rifling for 5mins in my bags looking for my keys, or a dummy, or my sanity, ya know?