Fine grain usually starts with a fine-grained film. It is the most important factor by far IME. The Adox/Efke 25 and 50 films have pretty fine grain, but not when compared to a modern film like T-Max. And the Adox/Efke 100 is not very fine grained at all IME.
I'd start with HC-110 for it's convenience and relatively fine grain. It has a decent amount of grain solvent if used at dilution B or stronger. Rodinal does not.