Clackey – I'm doing the same thing. A non-Marvel setting with ordinary folk who have developed abilities. For specialties we just chose them at D6, meaning "regular training", so they're not experts. Not yet. They'll have a chance to justify higher dice through spending experience and using those specialties in the game.
I have no problem with coming up with specific, custom specialties for players. I have no problem with the players coming up with them themselves, either – it's just one further level of investment they have in the character.
Perhaps even through RP they can add more specialties. If a hero spends time in-game hacking into computer systems, you could add the specialty of Tech (Networks) D6 as an introductory specialty.