I estimate we are about 10 turns from Liberalism right now. I think we should research Education and Liberalism now. We can then pick our free techs. The main options IMO are Astronomy (we need to make the Optics trade with Augustus), Printing Press and Nationalism.
Tech info (beaker count isn't accurate for our current game, but the ratios are the same)
Nationalism is already known to Gandhi, and I'll bet you 10 bucks he will finish the Taj Mahal wonder before we can get even close. Otherwise, the tech leads to Military Tradition, but we're quite a ways off from Cuirassiers or Cavalry.
Printing Press will give us +1

on every village and town, which is great, and it leads towards Replaceable Parts, and that in turn to Rifling. I think this is the best option.
Astronomy will give us access to observatories, but I think only Arkadia really can afford to spend hammers on that right now, other cities need to build units. It will also give us intercontinental traderoutes, for when we meet the remaining 2 civs.
I personally think we should do Education - Liberalism - Free Printing Press - Guilds - Banking - Replaceable Parts - Gunpowder - Rifling (straight Rifling beeline). This picks up grocers and banks along the way, to increase our gold output (especially in shrine city Madrid), and it leads us to riflemen.