Well, if you want an official XCOM pointer is that it seems that only the most powerful psychics can manipulate the physical world. Game-wise, only the Volunteer and alien Ethereals (both the most powerful units in the game, psionics wise) can actually cast a power that directly affects the material world. Most psionics is based on fiddling with the mind of your target, whether that's positive or negative. It's actually what psionics is meant to be in the first place.

 Of course, I'm not saying an elite unit of less than 100 people can encompass the entirety of psionic potential and variants.

If you make a psionic that focuses on manipulation of the material world, they could have a deficiency in the more emphatic powers, such as an inaiblity to cast Mindfray or Mind Merge, which are basic powers. I'm not sure how the whole thing would work, the GM could probably give you more details. This is just my personal take on psionics.