Izzywizz,
Welcome to CivFanatics!
The quick answer would be to say don't get locked into any particular formula or formulae, as each map will throw you different challenges, and your priorities will change during the course of the game. It's no good for me to suggest that Phiosophical leaders should sit in Pacifism for much of the game, because you might be desperately lagging in infrastructure and Organised Religion is your best bet - or you're weak and surrounded by warring religious nuts and no sooner do you adopt a religion than you may as well paint a bullseye on your forehead because if Isabella doesn't attack you, Saladin surely will.
So, with the disclaimer out of the way, all things being equal (just speaking of 'vanilla' traits) ... ;
Philosophical leaders will get more leverage out of running Specialists because it's quicker for them to 'pop' Great People. Representation, The Caste System, Mercantilism, and Pacifism are civics that are Specialist-oriented, either allowing you to run more Specialists and/or get more value from your Specialists.
Financial leaders tend to benefit from a Cottage Economy, that is; improving a high proportion of tiles in commercially-oriented cities with Cottages that can be worked by citizens. Civics that help here include; Universal Suffrage, Free Speech, and Emancipation.
Aggressive leaders will be able to quickly produce quality forces with a combination of civics such as Police State, Slavery, Vassalage or Nationhood, and Theocracy.
Industrious leaders will get a kicker from Organised Religion and Bureaucracy if building Wonders in the capital.
Expansive leaders can grow massive cities under Hereditary Rule, because it's easy to get happiness up through building units, while the Expansive trait provides your cities with health benefits. Representation is an alternative that extends happiness to your largest cities.
Creative, Organised, and Spiritual leaders have arguably less-clear civic-trait synergies, although maybe someone here might add something here. I guess it is worth noting that Spiritual through its 'no anarchy' gives you greater flexibility to 'chop and change' civics as conditions change in the game, while Organised leaders can run the expensive civics such as Police State, Vassalge, and Organised Religion cheaper than their non-Organised rivals.
My advice would be to keep experimenting with different play styles and victory targets. Also, keep reading the CivFanatics forums and check out some of the articles in
The War Academy.