Dhoomstriker's advice seems very good to me.
I especially like the part about getting more workers to chop faster. I don't think you need the extra workers right now but a worker burst will quicken your military build-up.
Regarding your tech path, you really do have the choice.
I don't think there are any wrong options, there.
- If you want to go for Military Tradition, you'll need Music. You'll probably need to self-research that. Although you could start with Nationalism and maybe trade towards Music. In such a sense, researching Education right now would seem unnecessary.
- For other routes, you need Machinery. To unlock Printing Press towards Rifling ; to unlock Engineering towards Steel. There, it's mostly self-research, isn't it ? Starting with Metal Casting.
Anyway I look at it, I think you'll need to research and backfill some techs.
It would make sense to look for trade baits as you don't necessarily want to let go of your Civil Service + Philosophy monopoly.
I think I'd favour the Machinery route because it would allow you to spam Forges, so as to get more production power. Also, no marble, as you mentioned, makes the Music route less appealing.
Speaking of production power... one Granary ? You certainly need to spam those. Do you think you've gained much by avoiding granaries ?
You've probably been able to work more cottaged tiles but this is very short term. Over ten turns, a granary pays off. Overall, I think you'd have been able to generate more commerce with granaries up.
In the same line of thinking : if you want to make the most out of Bureaucracy, Carthage should probably take control again of its corn.
From the position you're in, one thing you might consider is a civic switch to Caste System.
You'd have to ponder what Great Persons are appealing and how they can fit into a plan. Great Scientists can bulb (Education, Printing Press, Chemistry) ; Great Merchants can make trade missions (upgrade troops ; better for mounted units or canons than melee) ; triggering a Golden Age is also an option.
Caste System would stun your no-granary growth. Big loss ? Maybe not. That would let you chop your granaries so growth could resume after you've generated some GPs.
Alternatively, you could remain in Slavery a while longer. In this case, I'd focus heavily on establishing your production infrastructure asap (Granaries and then Forges).
Finally, I like the idea of an intermediate war.
A unit that hasn't been mentioned but could do wonders is the Maceman. Those don't upgrade to Cavalries but they're nasty with their City Raider bonus.
If you can catch a civ without Feudalism, they'll be easy pickings to a task force of Macemen (+ some siege in option).
An intermediate war wouldn't mesh very well with a Caste System switch.
It would fit better with a worker burst + Granary chops/whips and Forges whips in option.
If looking for a war target, I'd be very much attracted by the Temple of Solomon.
Greece is close by, sort of weak and has good land. You'd need to solve the diplo situation before getting involved in a war, so as to make it safe.
You're very much ahead as it is, except for your city count.
So the route you choose is up to you, you've got a wide margin for manoeuver. Simply, you need to tie together the decisions that make a route good.
(So if you go Mil Trad, you should pre-produce mounted units and aim to upgrade them via a switch to Caste System, so as to make up for your low production power, so as to make the most of your high population cities and the delay towards the war.)
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