My semi-serious answer is the era and campaign you most enjoy. One of the most delightful experiences I had with a long time PBEM player/friend was to start at the earliest game and play forward to the most recent game of all the scenarios and DLCs. It was a lot of fun. Then we went back to the ones where we thought we could do better. Then, we switched sides, that is, I was not longer not Rome, but Rome and we did it again.
Still we are not sated in PBEM play of this AGEOD gem. So now we are replying the eastern fantasy scenarios.
If the two of you are on this project without a third player, there are some games which are best played with one of the players taking two factions, like the Marius v Sulla game, which is a great PBEM game. But the Marius player needs to take Pontus also to balance play. Other scenarios are ok with a faction in AI. Look at the scenario info to see if two factions mutually hate the third or if all three are in competition.
If I were just to pick one, it would be Marius v Sulla, but the Second Punic War would be next, really complicated and fun. Start dates are open to your preference. I do not know which start date is best.