Hi Rags, and welcome.

This problem rather depends on what you are making.  It is fundamentally one of physics principles.  If you are building figures you must work out where your centre of balance and main weight lies and then position the base structure directly underneath that.  Have a look at public sculptures, human figures are usually standing with feet well apart, or leaning on a broken pillar etc, the base on the plinth is usually wider in diameter than the extremities of the statue.  The same is true of equine (horse) sculpture,  especially rearing horses.

With Papiermache you have this basic problem of physics and gravity, which is made more difficult by the fundamental light weight nature of the medium.  It helps to increase the weight at the base of your piece, I often use plasticine in the armature, but you could use anything to hand that has a good dense weight and wont degrade over time.

Alternatively think about the most stable structures, tripods and four legged objects and see if that applies.

This is a real problem in the display of puppets and art dolls, have a look in the gallery and on the web at sites and see what solutions other artists come up with. Some of these may well help you.

Best of luck, what is it you are trying to get to stand up?

Newmodeller has covered most of the problem.

Something like your Goblin could have extra-large feet, weighted down inside with lead fishing weights. The more area flat and/or weight on the ground, the more you can get away with above.

Sue