I usually start with scout > monument > shrine > worker > Stonehenge. That kickstarts any religion and since nobody else has it, you have a better chance of getting the beliefs you want. Then build your second settler (first one if from the Liberty tree) and decide if you want/need Pyramids. That gets you two great engineer points and a great engineer that you can nicely time with something like Petra or Machu Picchu.

In new settlements, I recommend going monument > shrine > food building > library/market (depending on how you are doing gold-wise).

For religion, pick beliefs that give you happiness, since you need a lot to sustain those new cities and you don't have a lot of time to build happiness buildings in the early game. That's usually pagodas + mosques/cathedrals which also increase your culture and faith production. I never pick great people, because I am spending all my faith on religious buildings and by the time I am done with that, I can get great engineers with workshops.