I find that IND *shines* on Immortal.
Spamming wonders without it requires some serious concessions unless you have the appropriate resources; on lower levels where you don't need it you might as well pick PHI (faster rewards, more flexible).
Spamming wonders is still attractive:
The Great Wall is at its most powerful here. Below you don't really need it, on Deity the biggest menace is over before you typically finish it.
A quick Oracle/MC fix is a great asset to gain tech equality or even superiority right from the start. It's less expensive in terms of citizenturns to research the religious line and build it than it is to research Metal Casting, and with IND gives you a decent edge in production as well.
On some maps, the Great Lighthouse becomes a huge asset, the Great Library is pretty much always a good investment and the Pyramids remain a strong option depending on your playstyle preferences. Even many of the less popular money can be great: The Hanging Gardens for example allow you to transfer production from an established to underdeveloped cities (by providing whipping fodder); very useful for making the latter assets rather than liabilities.
While overflow money was limited, there is still compensation cash. Losing a wonder race might not be so bad at all.
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Traits roughly in order of preference. I love:
ORG (makes expansion/war affordable while you keep focusing on hammers, some nice discounts)
IND (see above; snagging a few high-impact early wonders is both beneficial and difficult without)
FIN (Inferior to ORG early on imo but I currently like to replace production with rushbuy in the Renaissance)
PHI (never bad. Allows a great W/SSE if you start with wonder resources deep Liberalism beelines)
I'm fine with
IMP (On Immortal, I favour getting settlers out faster over getting cities developed faster because I sometimes need to beat the AI to juicy spots. Recovery can come later.)
SPI (Great diplomatic tool if you can appreciate it... imo much more useful on Deity).
EXP (Generic faster start... not bad but on Immortal I prefer something more 'assertive'.)
CHA (not bad, but I care more about production than early vertical expansion.)
I actively dislike
CRE (convenience instead of power. There are many workarounds for a lack of culture.)
AGG (normally the bottom trait for me. On Immortal, it at least makes a forced rush easier)
PRO (Generally not needed; defensive warfare becomes more attractive on Deity).
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Leaders:
With a military edge, it's still possible to establish a dominating lead in the classical age. Especially nice if you have long-term economic benefits to make the best of it. Expect the usual suspects: Huayna Capac, Darius, either Roman or Egyptian. I'm also very partial to Mansa Musa (Skirmishers: resourceless emergency rush unit, ultimate choker, unbeatable defender and cost-effective general purpose unit until late medieval age).
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Regarding religion: If I can pick up Judaism, I will... mostly because I love Organised Religion. Not reliable at all unfortunately, because the AIs can get too much of a head start from goodie huts (not only are they more likely to get them tanks to their starting units, the get better results).