Which glue should I use for fabric-shaping?
You have quite a few options:


PVA (polyvinyl acetate) glue (a.k.a. 'school glue', 'wood glue', or 'carpenter’s glue'; a type of white glue that dries transparent. Furthermore, it's non-toxic, easy to apply, affordable, has water resistant variants (that deter mould and the like), fast-drying, and has a high holding strength. source


  Dilute the glue using equal parts of glue and water and mix
  continuously to obtain a paste with an even consistency. Apply the
  glue with a paintbrush. Craft the fabric into the desired shape and
  leave to dry. Apply more coats, depending on how stiff you want your
  material to be. 
  Another way to stiffen the fabric is to immerse it into a bucket filled with diluted glue. The solution can be more or less concentrated, depending on the effects you want to obtain. Squeeze the fabric to remove the excess solution, shape it and allow to dry. source

GAC 400 (from Golden Artist Colors; an acrylic polymer). A commercial product specifically aimed at giving permanent shape to paper and fabrics:


  Stiffens natural fibers and fabrics and is useful for stiffening
  unprimed canvas or sculpting and shaping fabric. Fibers saturated with
  GAC 400 will dry to a hard, stiff film. source


It can be heat-set, to increase its permanency and stiffness.
Fabric stiffeners for crafting purposes (like Mod-Podge 'Stiffy' (great marketing there)). Apply with a brush onto the shaped fabric, or immerse the fabric and directly apply it to the mould. 
See here and here for examples.
Wallpaper paste (methylcellulose). Again: apply with a brush onto the shaped fabric, or immerse the fabric and directly apply it to the mould.
Liquid Starch (corn or potato starch, or commercial products such as Sta-Flo). Mix with water, and, again, apply with a brush onto the shaped fabric, or immerse the fabric and directly apply it to the mould. Apparently this is also used to give denim jeans heavier wear (fading/creasing). This post on that process shows a pair of jeans standing up by themselves, so I guess this a good option. Here are some recipes for making the glue.
Skin glue: another traditional, organic, gelatine-like glue, made from skin and bones of rabbits, hares, and other animals. It usually comes in small grains or powder, which can be found in artist shops. Mixing it with water and heating it up yields a very strong, slightly yellow drying glue. I use it regularly in my artistic work to stiffen fabric, and it's wonderful stuff (as long as it doesn't go bad). See this link for more information on the preparation (and/or ask here if you have any more questions). Once more: you can soak the cloth in the glue solution, or apply it with a brush. It is, however, relatively sensitive to moist.
Epoxy resin: more information following.