So I've been thinking of going a war\culture generation route with Songhai, since the Tabaya can assist in generating culture if you're near a large river. So far, the idea is to go Authority, then Aesthetics, but I'm having difficulty thinking of the last policy, and what ideology would be best. Rationalism allows me to stay on the cutting edge with my army, while Industry allows me to crank out units and buy units. As for ideology, I figured Order would give me the best of both worlds, in terms of culture and fighting.
Any tips?
Besides these sound advices, the third tier of policies will depend on what you achieve. If you empire is happy, more or less well developed with many villages and towns and you don't plan on further conquests, then Rationalism. If you want to keep up the fight, you have enough and well trained units, but you are struggling to maintain the infrastructure, then Industrialism will get your buildings built and your budget full. If you want to keep fighting but your army sucks in comparison, want to focus on domination or you end up with many island cities and farms, then Imperialism.
Going from Authority to Aesthetics is a little weird if you are not Japan, it calls for crippling wars. That is, most of your fights are for pillaging (Songhai excels at pillaging) and making other civs waist resources, not for conquer. You may conquer one or two civs, just for the fun (and their wonders). Long wars and overexpansion hurt happiness, and aesthetics has a policy that turn excess happiness into culture but doesn't help in being happier (intended for smaller and well developed civs). But if you don't keep killing things, Authority will yield lower culture and science than Progress.
In the case you end up conquering early those 2-3 civs (by standard size) and then stay of middle size pushing your culture up, and fighting here and there to remove competition but without further conquests, I'd say you'll continue better into Industrialism and Order.
Take down first the civs that have higher tourism output and you'll get advantage fighting the others (they'll be easily influenced and you get a bonus when fighting influenced civs). Also you will be able to focus on tourism uncontested.
EDIT: Going Tradition is a thing you might consider if you don't have too much place to expand or want to leave the conquests for later (when you can make use of your unique unit). It will give many great people that will yield even more thanks to Aesthetics. But you won't be working many ground tiles late game.