Here is my first attempt at a mecha for Mobile Frame Zero, made with Lego I had as a child. This was primarily an initial investigation into simple joints as these will be important in any mecha. I got my initial ideas by looking at some of the mecha designs on Mobile Frame Hangar.
Firstly, you can get quite a lot done with single-pip pieces. They give a single degree of freedom because they join with a single peg in a hole, so can be rotated. The tops of the legs, for example, are just single-pip blocks, so can be turned, and the feet have a single pip on the top, so they can be rotated to make it look like the feet point in or out, which also improves stability.
The shoulders are a combination of Space Positioning Rockets (3963) (details not available on PickABrick) and Angular Bricks 1x1 (4070), although there are many other parts that could do the same job. Note the the rocket parts provide mountings to the side (for the arms) but also to the front and rear, giving a way to add all sorts of other systems to the mecha.