I have a large canvas tote from the local thrift shop. The straps are the same type as you'd see on a large back pack or the aluminum frame pack we use for camping - can carry a lot of weight and the strap/canvas not tear. Machine sits nicely in it. An option might be to buy 1 inch heavy straps & sew them on to a large sturdy bag - down each side & around the bottom - to assure strength for your needs. Timtex or cardboard sewn into a fabric 'pillowcase' would keep the bottom of the bag flat.
I'm all for spending less and still getting something sturdy in the bargain.