With the exception of Islam they're religions the human player actually has a good chance of founding. Founding one of the earlier ones cripples your game even if you manage it. If you have non-religous AIs you might not even get any religons at all. Confucianism is the one that someone playing fairly standard can achieve. You can oracle CoL, or bulb Theo/Philo. But it really only plays a big role if you're trying to AP abuse. Egypt can be pretty adept at it thanks to their unique building that can run priests, allowing a fast theology bulb. Whether or not that's a good idea is up to you.
If you have a neighbor that you don't like, you can gift them a few missionaries and don't adopt that religion; chances are they'll get hated and you'll get a chance to collect some sweet shrine gold. This is the best way to put annoying pe
You don't want to found too many religions because you should leave it up to the AI to spend their hammers spreading religions. Getting your own makes it harder for the AI to give you religion as having a religion present blocks autospread and also increases missionary failure rates. This is why getting one of the first 3 is an awful choice most of the time even if you can get it. Especially earlier games where production is lower and it's physically harder to send missionaries due to barbs, lack of roads, etc. This means the first few religion spreads are crucial as it takes time to build up the +diplo for shared religion. It could be the difference between them plotting against you or getting them to pleased and making things easier.
If you want to spread some, do it to their biggest cities and they'll eventually do the work for you. Also, lovefests are good for your side; not so good on the rival end of the world. Ideally, you want your side of the world to be a lovefest to increase your tech rate, while the uncivilized bumpkins on the other side make for easy targets once you're done betraying your former friends or not.
One funny thing that can happen is if you can box in a religious AI, especially they have mediocre land you don't want for yourself. Them remaining small and creating the dominating religion is one of the best things that can happen to you as you can turn them into your NotVassalButEffectivelyOne non-factor that will help you win the game. Make sure you don't let them build the AP. Otherwise there would be a bit of violence.
This person is usually Isabella....
As for Divine Right, it houses 2 wonders; neither which will come into play in a regular game. I can imagine Versailles being a thing on maps with many landmasses but then there is state property.... Honestly, it's one of those wonders where you're better off capturing it.
Finally, note that you can switch religions while building the AP as long as the target religion is in the city that builds it. Spiritual Civs or Civs with a Golden Age can do some funny stuff. So say everyone likes Buddhism. You start building the AP and found Taoism, then use the missionary to try and convert that building city. If it succeeds you can switch over to Taoism just before the AP finishes, and switch back to get on everyone's good side. On Prince, you can always found Christianity and Taoism without a beeline. Doing that will discourage them from getting the tech for a while as they can no longer found Christianity and lets you more leeway as it is very annoying when missionaries fail.