Start with Ilford's recommendations. They recommend DDX and Microphen for Delta 3200 because these are both fairly active general purpose PQ developers that will give you excellent image quality, but a little more speed than say D76/ID11 (with only a slight increase in graininess). If you want a home mix option, try Ilford ID-68, which is a Microphen-type developer.

If you have already been using a home mixed D76, no problem using it with both HP5 and Delta 3200. For Delta 3200, use Ilford's recommended time for stock D76/ID11 and adjust from there if you want to dilute it 1+1 or 1+3. Keep in mind these fast films are inherently lower in contrast than slower films so some experimentation will be required with dilute developers.

I would not bother with D23 (or speed losing variants such as Perceptol) or the other home-brews OP specifically mentioned. Better off overall with D76/ID11.