I'd like to give my two cents on what to build early.
From the beginning, you will have 6 things unlocked that you can build already, without any research! You can build a Monument, Settler, Builder, Scout, Warrior, or Slinger (or your civ's unique version of one of those things). Unless you are playing as Kamehameha, you won't be able to build a Settler first, but you probably can for your second choice and definitely for your third.
Let me go over what's best and when to build it, generally speaking.
1. Monument. Monuments give loyalty per turn and culture. If at full loyalty, you receive more culture. Culture is used to unlock more civics on the civic tree. A city's culture also helps it expand faster, giving you tiles around it for free. Civics are very good and monuments are nice...however, there are much more important things to worry about early on besides unlocking more civics. Monuments seem like they do a lot and will help you get a jump start, but it's a noob trap. In actuality, having more units to explore, more cities, and more productive cities will all help to increase your culture as well.
2. Settler. Settlers can only be built in cities size 2 or higher. They take 1 population away from the city once completed. They are, obviously, used to found more cities. This is important to do quickly on higher difficulties, however, since you're new I recommend playing easier difficulty levels as you learn the game better. Playing on Prince difficulty or easier (maybe even King), there's no rush to build cities. Barbarians are always going to be a problem and combat might not come naturally to you. On higher difficulties, I recommend building a Settler as the second thing in your capital and then virtually spamming them in your capital until you have 8-12 cities. But for starting out, you can wait a bit before you begin expanding.
3. Builder. This is something that I'm not sure why people recommend it so early. Chances are, there's no tiles nearby your city you can even improve. Maybe 1 at best. It's a waste of time to build a builder early. Not in your first 20 turns, for sure. Either you won't have the technology yet to improve the land, or you won't be able to clear the forest/jungle there, and your citizens would be better off working land that is impractical to improve early (such as Bananas in the Jungle, for just one example). You shouldn't build a builder until you are comfortable with your military/scouting, have a few cities already, and then it's like "ok, what now?". If there's enough viable places for you to improve, it's not a terrible idea for you to buy a builder with your first 200 gold but this should by no means be set in stone. Every game is different and when you start going for builders is going to be one of the things that should vary greatly from game to game.
4. Scout. I almost never build scouts, unless maybe I'm playing a civ that excels with them. They are weaker than Warriors and Slingers. If you want, you could MAYBE build ONE as your very first thing to get exploring faster, but they can easily get suck by Barbarians and they aren't always going to be faster. Barbarians also kill them easily. Instead, I'd recommend building something else first...see below.
5. Warrior. Warriors are the strongest unit you can build in the beginning. If you fear the Barbarians and aren't comfortable with combat, build Warriors early. Make sure to have at least 3-4 before going on to something else (probably Settlers).
6. Slinger. Slingers can attack on your own turn without receiving retaliation damage, but they take more damage when attacked on your opponent's turn. They upgrade into Archers, which can attack from 2 tiles away. If you feel comfortable with combat, I'd prioritize these over Warriors and have at least half and half, but focus on Archers over Warriors.
What about other early things you can build?
Generally speaking, you should ignore them until you have a military/exploring backbone and a few cities out.
Holy Sites should be ignored entirely for a new player in my opinion. Only start building these when you feel ready to try something new. Ultimately, many people playing on the hardest difficulty completely ignore them anyway, unless they have a specific reason no to.
Campuses are a certainly more important, but it will take a lot of building before it gives you enough science to matter. Again, focus on other things first.
Granaries aren't very useful compared to other things you can do. You can consider buying Graneries with gold in newly built cities if you can afford it and want them to get a jump-start to growth. But this is by no means necessary.
Galleys can be useful to explore with if you are on a small island. Otherwise, I'd skip these until the mid-game.
As far as what techs you should focus on early? I think lotrmith has the right idea. Animal Husbandry first always always always. Because this lets you see horses. If horses are in your capital, now you can work them. If horses are nearby, you can build a city near them. You can use the horses yourself to build Calvary units OR sell them to other civilizations. Similarly, you can start heading for iron working next to do the same with iron, but because you want to trigger as many Eureka! as possible, it's ok to wait a little bit on that one. Chances are, you'll have Iron Working before you start building your 2nd city onwards.
Where is the best places to found a city? I recommend looking up guides for this, but here's some good rules of thumb: Your city center will always give 2 food and 1 production. If the tile it is on gives more food or production, it will grow to match it. But without floods and volcanic eruptions, 2 food is the highest (because you will have to clear whatever is on the tile to place your city) and the most production you can get is an extra +1 from being on a plains hill. So a plains hill is better than anywhere else to settle a city, but if there isn't one close then just ignore that. Keep in mind though, the same rules apply for desert, snow, and tundra. Generally speaking you don't want to settle near desert, snow, or tundra; these tiles like to stick together, and they are bad. But if there's a lone spot of one of these it's not a terrible place for your city as it will still have 2 food, 1 production.
You should also try to settle on fresh water if possible, and if not, then within 1 tile so you can get it later with an aqueduct. Fresh water comes from rivers, lakes, oases, and some natural wonders. Mountains also provide fresh water with an aqueduct. Worst case scenario, I'd put my city adjacent to the ocean's coast. This will provide a LITTLE bit of water but Fresh water is the best. Fresh water allows you more default housing in your city, letting it grow more before you need to find ways to increase housing.
As konokono suggested, try and place cities near resources. Placing your first city you won't see strategic resources yet, so prioritize luxury first and bonus second (it tells you if it's luxury or not). Bonus resources tend to give food while luxury resources tend to give gold, and food is more important than gold. So if you find a bunch of bonus resources and no luxury, it's not the end of the world. Just make sure to settle your 2nd-4th cities near new luxury resources.
Another tip: Sell luxury resources to other civs early, since you won't need the happiness/loyalty yet. You especially want to sell if you have multiple copies, as only the first copy you have is even benefiting you! Some people will even recommend founding your capital ON a luxury resource, as it will give the resource right away so you won't need a builder to work it. This way, you can sell the luxury resource early to another civ. This method has its downside though; you'll never be able to get the bonus gold from having it built up if your city is built on it. Keep this strategy in the back of your mind if you want, but I wouldn't prioritize it when choosing where to settle.
Well, I hope that all helped! Let us know if you have any more questions.
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