I have cut the 3" drain pipe at the concrete floor level but the flange will not go all the way down to the floor. It rests about 1/4 inch off so when I mount the toilet on the flange, the toilet won't rest on the floor, it too is about 1/4inch high. Nothing has been glued or set permanently yet.
Do I need a different type of flange, do I have to somehow cut out more drain and concrete to get the flange lower (a very hard job) or do I put some type of supports around the bottom of the toilet bowl for it to rest on and be stable.

What type of 3" pipe are you using and which flange. They are not all the same.

It sounds like when the plumbing was roughed in it was intended for the floor to be tiled before instalation of a toilet, I would recommend that you tile at minimum the area directly under the toilet before permantly installing the toilet.

Buy a flange that has no stop. That way, you can push it all the way down. Also, have piece of wood and mallet ready. After you insert flange on pipe, put wood over the flange and gently top it with mallet.