I solved my problem. I liked the idea of a Dremel and a drill press stand, but didn't like the grumblings about the rigidity of the stand. I know some have claimed the older stands are better, but didn't want to mess with it. So, I found another company that makes rotory tools and a nice sturdy stand. Proxxon, which I know someone here has mentioned, makes a very nice rotary tool, and a very solid stand, although with a bit of "made in Taiwan" cheapness. But the stand is solid as far as drilling is concerned.
BTW the rotary tool doesn't seem cheap at all, and is made in DE and LU.