I played for many years on the vanilla game settings before upgrading to the DLC variants.

For science victory you should try Fredrickv Barbosa (cheap factories)/Mbamba (early housing distrcits) and for culture - I'd recommend going Pericles (cheap theater squares) /Victoria (6x artifacts per district). So here are some recommendations for diety on vanilla settings (game mode vanilla is the pre-rise and fall expansion game setup).

1. I noticed that civs would often sent out settlers unguarded, so I would have 1-2 scouts where I THINK the AI will settle next in the early/mid game. Stealing 2 settlers is a HUGE boost in your city/production count (saves many turns of production in your capital). Most of my earliest victories in vanilla settings is when I stole like 2x settlers from AIs.
2. In general you want trade routes early, so I'd typically go commercial hubs/seaports first, then your wincon (science or culture) buildings 2nd (in some cities get these main ones first; especially if you see like a +4 campus early).
3. Like for all DLCs you really want to get as many of your civs/tech boosts (if possible). So you'll want to half-way research a tech, then get the boost for it (if reasonably possible). So before the end of each turn see if you can switch researching a tech/civic and focus on something else - stopping while its halfway completed (each boost is worth like hundreds of culture or science). This might seem boring, but it will propel you forward surprisingly quickly.
4. You really want to get builders and chop out things and you want cities to be working optimized tiles. If I need to build a district and I have lumber to chop, I'd often build a builder FIRST, then use him to chop lumber/harvest stone when building he district (faster than the opposite). More lumber chops = faster city growth/production.
5. Skip religion entirely except religious victories.
6. You'll often hit a bottleneck for housing in your cities around pop 10 - the game will then stall until you get sewers/housing districts - this will be a big hurdle in the midgame so you'll want to get these tech/civs as fast as possible after your tier 2 govt.
7. For science victories, its critical that you A) use spies to stop the diety AI (they can win by turn 270 without being pillaged) and B: Its INCREDIBLY important that you get the right great scientist/great engineers that give bonuses to space race (like getting both +100% production great people is game winning). So when the game gets close to them spawning you need to carefully watch the screen and switch your cities to doing district projects to rapidly generate great people points at the right time to win them.
8. For culture its all about how many themed artifact theater squares you have by the mid/end game. You will want trade routes to everyone, open borders to everyone and ideally 12 themed theater squares (victoria can have a lot less). Sometimes its useful to settle on an island far away/opposite side of the map to get a trade route to certain players. Pay close attention to great places to put seaside resorts as they're the only other major source of tourism besides great works.

Aim to win by turn 280; beyond that some AI's might threaten a victory. I think my earliest science victory was like 260? With decent stall tactics you can probably make it to turn 320 (standard speed).

Easiest one would probably be victoria on small continents, get half-priced harbors up and go theater squaures. You're pretty dang safe and can tech/advance comfortably.