The choice is based on how dominant you expect your civ and religion to be. Peace loving allows you to gain happiness from followers, even if you aren't the dominant religion in a city. Ceremonial burial requires that you be the dominant religion. Therefore, if you intend to put lots of effort into making your religion dominant by using inquisitors, GPs and missionaries, then use Ceremonial burial. If you are content to let your religion spread organically, use Peaceloving. Both do work on City-states. Additionally, CB gives a more immediate benefit, while peaceloving takes time to expand outside your borders. CB works on your own cities, while PL doesn't, so if you are dominating the game, choose CB.
In conclusion:
Dominant Civ and/or Religion: pick CB.
Lagging Civ and/or Religion: pick PL
Immediate need: pick CB.
There are a lot of factors here, but I do find in most games there is sort of an ideal build order for the first few moves of the game.
Your Settler should generally plop down on the tile you spawned on. If you've got other units you could move, you might let them move first and consider moving one tile or maybe one move's worth around before you settle, but I'm of the impression that you should really settle quickly. Usually you start on a good tile. But I digress...
Your starting military unit should make expanding circles (or arcs, depending on the geography) around your first city. The idea here is to find the sites for your next cities.
In your capital, build a Scout. The only reason you might not want a Scout is if you are pretty sure you're not going to get any ruins with it early - you're on a tiny island, for instance.
Second, build a military unit. You're going to need a unit to defend your borders. You might not want to do this if your initial unit explored quickly and is back home, but if they're taking their sweet time and there are barbarians about, you're going to need another fighter.
Third, build a Worker. The Worker should hang out within a turn of either the unit you created or the city itself. Focus on connecting your "special" tiles, starting with luxury resources.
From here it kind of depends on what the situation is. I like to start building a Settler fairly early if I found a good site for another city, but I will also put a few turns of production on something else (or make another military unit, etc) if I'm close to getting another population in the capital.
The Settler should go with the Worker and at least one military unit to found a second city as soon as possible.
After the Settler I'll tend to produce another Worker (to replace the capital's worker) and perhaps another military unit depending on the level of hostility around.
The Monument in the capital can wait a bit, the Palace generates culture so it's not 100% critical in the capital. If the map is very large and there are a lot of ruins to gather, another Scout may be worth it. Your tech and social focus also starts to come into play from here on out, and that will determine what units and buildings you're going to focus on in the next 50 turns or so.
The general reasoning is that early military units are more or less useless - you're unlikely to get to the point where having 2 versus 3 Warriors is the difference between winning and losing. You're also unlikely to be in a situation where +1 culture is going to make a big impact in the long term.
However, having a Worker, protected, at your capital, and an early second city with a second Worker are both very, very big deals. You can get a pretty good head start this way.
Best Answer
While you do have to produce something, there are a couple of techs that give you alternative options to using your production on units, wonders, or buildings:
The technology Currency unlocks "Wealth" which converts a percentage of your city's production directly to gold. Similarly, Education allows you to produce research. These two options are typically below the wonders group in your production menu.
You can also change the focus of your city away from production (to food, commerce, etc) which will slow down your production, while providing alternative benefits to your civilization. Changing the improvements on your tiles can also shift the focus of a city from production to some other use - for instance, chopping down forests or demolishing a mine will reduce the production in a tile.