Walmart has branded ones, no worse than hefty ones and a little cheaper

You need bags that would be durable, tear and puncture-resistant. Such bags would be able to hold all kinds of construction waste, including sharp objects, pieces of rocks, and so on.  I recommend choosing the ones made of Linear-Low Density Polyethylene. This material is really durable, and you won't have to worry that the bags are too thin. Check out bags made by interplas.com. They meet all the requirements, and I usually use them in my construction work. I just buy a dozen of such 55-gallon contractor bags and don't have to worry about a place to put the garbage.