The force will of course vary between different objects, but that's a non-issue; it already does that here on Earth and in other gravity wells, as the gravitational acceleration is more or less constant at sea level, but people (and other objects that rest on the ground) have different masses and thus exert different forces upon the ground. Getting the acceleration close to 9.81 m/s^2 at the ring's "floor" is what's critical, not the force each individual is applying to it, as that is only a function of their mass (which is constant) and the acceleration (which we can determine by changing the ring's radius or rotational speed) given by the good old F = ma.
Another thing to note: If the radius of the ring is very small compared to the height of the objects you want to experience about 1 g (i.e. the people aboard your space station), keep in mind that they will experience different acceleration over the length of their bodies, since anything closer to the centre (heads and such) will experience a different centripetal acceleration a given by a=(v^2)/r; you can get away from that issue by making the radius of the ring large in comparison to the people on it, so that the difference in acceleration between their heads and feet will be insignificant. Shouldn't matter all that much, though.
