c_trace(my.x,vector(my.x,my.y,my.z-200),IGNORE_ME | IGNORE_PASSABLE);
if(trace_hit && target.z > my.z+my.min_z-10)
{
I'm on the ground, respectively floating 10 quants or less above the ground. Some kind of a height buffer is usually a good idea to avoid the computation of unnecessary collisions.
my.speed_z = 0;
}

Ah, I was thinking I should use c_trace, but was once again scared away by the "slow" speed. Thank you, yet again!

c_move is based on c_trace with USE_BOX, thus c_trace without USE_BOX is faster than a c_move call.
c_trace is probably the most important Gamestudio function for all games, don't be afraid to use it. That means, use it whenever necessary and avoid it whenever possible. There are a lot of options to keep c_trace fast (use the IGNORE_... commands, keep the trace short, only use USE_BOX when necessary and so on).