Assuming you already have Hunting, going Poisons directly is a little faster than taking a detour through Writing. (And that's assuming the Library is built instantly.) I had a brief look at the lightbulbing charts and there didn't seem to be a reasonable path to help it. If you can pick up an early Great Person, just make a Sage and build Academy.
Poisons can be reached so early with teching that your capital city location probably matters the most. You need fast access to bonus commerce through Crafting, Mining, Calendar, Fishing or Education. Mysticism is good for the Elder Council and Academy from Great Sage, but don't rely on that alone. Once your commerce is figured out, consider Writing --> Hunting --> Poisons. This tech path does leave you vulnerable due to Hunters coming out a bit late. Going warrior-heavy and still being a little weak in power chart is common for me...
If you want to compete for FoL then get Hunting earlier and try to bulb it with Great Prophet when you have Mysticism but don't have Mining yet. (Otherwise you get RoK.)