You seem to be a bit indecisive about where to go with this game, so I'd advise against lightbulbing. In my experience, lightbulbs are best done with a specific goal in mind, and you've been hesitant to commit to a particular strategy. If you do go for a machinery lightbulb, make sure you're ready to take advantage of it right away.
I'd settle the GE in Mecca myself. It's 3 hammers, 3 beakers, +3 more beakers under representation.
Mecca is already your best science city (44

/turn in your screenshot) and if you head for CS/Bureacracy those hammers will be multiplied as well.
If you do go down the Machinery route, I would look to pick up Feudalism and Guilds ASAP, then use Serfdom + your improved worker micromanagement to get some improved workshops going where appropriate.
Finally, if you can't see a clear way to victory yet, it may not be a failing of ours; It might simply be unclear at this point. You don't have a tech lead but you do have a lot of land, you're protective, you have stone and the Pyramids. I know that attacking early often has the best rewards, but maybe a later push with drafted protective rifles would be the right move in this case. I'm not positive about that, but it might be worth considering unless you're confident that you can take out (eliminate or sufficiently cripple) Zara in one stroke.
It might not be an ideal situation, but I see your advantage lying in the amount of land you have compared to your neighbors, and the number of cities you can get before Rifles. All you need are Granaries, Madrassas, Courthouses, Walls and Castles.
Running a spy specialist in each city will give you 1+3

plus 4 espionage points. Madrassas give +25%

for 5

and cheap walls+castles give +25% espionage for 5 espionage per Spy Specialist. That ought to give you respectable research on your own while also giving you excellent intel and the ability to steal a few choice techs.
That would let you build up your economy right now, while slow-building an army of siege, adding camels to the mix when you get them, then quickly drafting an army of rifles.