This Claw Machine costume for my daughter was made with cardboard, a chain, small-sized stuffed animals, tin foil, a sink plunger, battery-powered string lights, duct tape, paint and wooden letters.
I made the frame for the machine using cardboard/foam board and black spray paint. I had plexiglass for the front window, but it proved to be way too heavy, so I bought a poster frame and used the plastic insert instead. A small box was used for the control panel and a sink plunger from the Home Depot is inserted most of the way through the box and the handle (yellow) is sticking out as the joy stick. I used a glitter poster board as the back of the machine (behind her head). There is a shelf inside the box that we taped the stuffed animals onto. The claw was fashioned out of tin foil and attached to a piece of chain. She dressed as a cat stuffed animal (you can't see she's wearing a tail).
One downside to this costume is it was difficult to walk in and she said it was the most uncomfortable one she's had (they've all been homemade and are fairly uncomfortable, but this was the winner as far as discomfort.) Got lots of praise though!