Like the game, you're limited to one ability per section of the body. The availability of the gene-mods will be a mix of EW and long war, and will largely be linked to which aliens Leon has gotten his hands on. Here are the ones available right now:
Hyper Reactive Pupils (Eyes): Will allow your character's eyes to quickly adapt to situations, not only giving them a better chance at hitting targets they miss, but allowing them to quickly find enemies that shoot at them from hiding.
Depth Perception (Eyes): Will let your character take full advantage of having the high ground, and they won't be as debilitated by the distance that comes with having a height advantage.
Smart Macrophages (Brain): Available thanks to the Sectoid autopsy. This supercharges your character's immune system, letting them heal almost instantly from being poisoned, and increases the healing power of medkits on them.
Muscle Fiber Density (Legs): Available thanks to the Thin Man autopsy. Grants super-powered strength to your characters legs, enhancing their jumping power. Will allow them to jump to great heights unaided. Can be used to reach roofs or get a temporary height advantage, and allows for a quick burst of speed.
And on a final note, as I said, only one Mech will be allowed, but if none of you want to have a Mech, I completely understand. Personally, I wouldn't like the idea of my character losing their limbs either.