There is a vast variety of construction methods and materials and each has its own associations for the viewer and benefits and drawbacks. Here are just a few possibilities.

Plywood and wood in general make excellent construction material for robots, invironments or inventions as it is relatively inexpensive and readily available. It is easy to cut using common tools like jigsaws but it can be heavy and may not be appropriate for a mobile platform unless you are using very heavy duty motors. It accepts paint well and it is easy to modify after working by using common Phillips head sheet rock screws or wood screws to attach and wood putty to fill. You can upholster plywood with materials of all varieties. It is easy to work with plywood, but right angles which most commonly result may not communicate what you are working to communicate to your audience.

Fiberglass is an excellent material for strong and biomorphic forms and can be painted with car paint for very smooth finishes. It can be done over plywood as with Bondo though the drawbacks are the dust from sanding is quite toxic so check MSDS sheets and use with respirators and caution.

Welding can produce large open space frames or can allow you to create very strong support structures for other materials.

TIG welding is expensive and requires specialized equipment though you can TIG alumininum and steel with clean and refined beads and joints. MIG welding is less expensive and easier to master though the welding material splatters and can require cleanup with grinders and metal files. Both TIG and MIG welding require ventilated spaces to work though you can pick up inexpensive mig welders from most home stores like lowe's and Home depot. 

Plaster is an often, overlooked material and you can realize many wonderful forms by creating structures of wood or steel and covering them in chicken wire. You can push and pull the chicken wire, which I call tuning. You can them use saran wrap and wrap the plastic around the form. A fun technique is to use an adjustable spray mister and a sifter and by gently sifting plaster onto surfaces like plastic wrap around forms and then spraying the surface of the sifted plaster with water you can achieve a shell that you can then paint with acrylic paints. Plaster bandage can is also an excellent material and you can use the technique above with fiber or think about scrim to give it strength.

The work below which is called Watchers was about the power of ambient TV light. The work is constructed with plaster and pipes as an interior superstructure with rewired TV's and metalized paint on the  exterior of the form to reflect the ambient TV light creating a glowing quality.