Horacekenneth:

All things equal, a compensating/acutance developer would normally be best for pushing. They typically provide the highest film speeds to begin with, and when overdeveloping it is easier to restrain contrast. This can also be accomplished to some extent with diluted solvent developers, but in some cases such as D-76, dilution does not produce a true speed increase.

To maximize a film's real speed, most true acutance/compensating formulas tend to produce a small speed increase (not a push), and there are some solvent developers that do this too - typically they are Phenidone-based developers like XTOL, Microphen, DD-X, TMax.

These properties vary from film to film, of course. It also depends greatly on the amount of shadow detail/local contrast you personally prefer. I like full shadow separations, so for me, based on my testing I've never found so-called speed increasing developers to really give me a useful speed increase. What they do offer me is less of a speed loss with contracted development. Others might come to very different conclusions. Some people say developers like FX-1, FX-2, and some two-baths like Diafine give them a full extra stop or real speed above box speed with non-tabular films.