Civilization 5 is a game that you can sink hours and hours into, having fun with whatever civ you play, victory you go for, etc.
Though, it is definitely a game that seems a bit daunting at first. There can be a lot going on depending on whatever victory type you go for. What's the point of a unique ability? What about unit or building? What is this "building tall" sort of thing? Generally, you'll find just playing the game to be the best instructor, but this will be a guide on the beginning of every game. Unfortunately, Civ is a series that relies a LOT on the start you get, and some more than others can even make or break your victory. This will be a guide on the ancient era, and it will also go over some terminology you may need to know.
Before we get into choosing a leader/civ to use, let's go through all the other parts first since it should apply to nearly every consecutive game you play.
The map type will be your greatest influence on the effectiveness of your civilization, and thus your victory. If your Civ has unique units that are mostly naval (ex: Portuguese Nau) or have unique abilities that relate to concepts such as embarking (ex: Denmark), you will benefit a lot more from sea-based maps like Archipelago and Fractal. In general, most war-centric Civs will benefit from the Pangaea map. Though if you want a more balanced map that doesn't put any Civ at much of an advantage over another, Continents or even Earth will always work. If you have some DLCs pertaining to maps, there are also "plus" versions of some of these maps, though they are very hit and miss.
Map Size has more to do with how hard you're wanting to work and how much your computer can handle it, but generally. I'd recommend either doing small or standard. The more opposing Civs the harder it will be to win, the less the easier.
Difficulty is a bit misleading. Any difficulty below Prince (level 4) will give you benefits. It will take less time to build things, and especially on Settler (level 1) you can get some pretty "OP" bonuses from the very beginning. On the opposite end, any difficulty over will be mostly about giving your opponents advantages. You will find it harder to keep up with them. So why is it misleading? Because people are under the assumption that it means the AI is any different, which it is not. The only way to change how the AI will work is through the "random personalities" option in Advanced Setup, but that still does not do anything to make it more intelligent, just more unpredictable.
Game Pace is a lot similar in the way where it has a lot to do with how many turns it takes to build something, research, gain social policies, etc. This has a lot to do with your patience, though going quick pace on a war-based Civ is a little bit harder as your units will go obsolete sooner rather than later.
These are mostly miscellaneous options that are really up to personal preference and challenges. There is only one that I will note, which is "quick combat". When you're first new to the game, it may be cool to see the animations of your soldiers fighting barbarians, your frigates firing on cities, or your cities firing back. Though as you play Civ more and more, these animations kind of lose their charm. In the late-game, aerial animations ESPECIALLY take noticeably longer than all other animations. You don't have to check this off, but eventually you may want to consider checking off Quick Combat if you find yourself annoyed.
First of all, I'm not going to go over time victory. It has a lot more to do with how many cities you spam rather than any actual strategy. Second, this is a guide more about the "Brave New World" DLC, but if you don't have that DLC just keep in mind the victory types are acquired quite differently. I'll briefly go over those along with the BNW explanation.
Domination: In BNW, Domination victory is about controlling every Civilization's original capital. It is the simplest victory to understand, but a lot of hard work to pull off. In Vanilla/Gods & Kings, you simply need to be the only Civ in the game that retains its original capital. This means, if another Civilization manages to capture all capitals but you capture theirs, congratulations, you win.
Science: Science victory is no different between each DLC, but is a little harder to come by in BNW. To achieve this victory, you have to research all the required technologies to build spaceship parts. Once you achieve all required technologies and build all required spaceship parts, you combine them all into the capital to achieve a science victory.
Diplomatic: Although between DLCs acquiring the victory is slightly different, the overall concept remains the same. To achieve this victory, you need to be elected as "leader of the United Nations" via acquiring a certain amount of votes. In Vanilla/G&K, a player (ideally you) needs to build the "United Nations" world wonder to first trigger the victory type. To acquire votes to be elected, you need to achieve ally status with city-states which can be done via quests and gifts. Other ways to acquire votes would be to build the aforementioned "United Nations" wonder, or by liberating city-states.
In BNW, the United Nations simply just replaces the "World Congress" at either when one Civ reaches the Information Era, or half of the Civs reach the Atomic Era. Acquiring votes is basically the same as before, though instead of the "United Nations" wonder, the two extra votes can be acquired via the "Forbidden Palace" wonder which requires you to adopt the Patronage social policy first.
Culture: This is the victory type that changes tremendously depending on whatever DLC you are playing. In Vanilla/G&K, it is very straightforward. You need to acquire enough culture to be able to fill up 5 social policy trees. Very simple, though keep in mind that it is much harder to achieve this with a "wide empire" (a Civ with many cities rather than few, populous ones).
While Culture still matters in BNW, the victory condition is considerably different. Instead of being about having 5 social policy trees filled, in BNW it is now instead about achieving "influence" over other Civilizations through Tourism. Your own culture fights against opposing Civ influence, and you can convert some of your own culture to tourism through buildings like the Hotel and Airport. In my opinion, this is probably the most difficult victory type to truly understand so I would probably refer to this guide for more.
No matter which DLC, however, your cultural victory strategy will often be based around generating Great Artists/Musicians/Writers, and creating "Great Work" slots via certain buildings.
First of all, I'm not going to give a guide on how to play each and every Civilization in the game. If you want a really good guide on the ins-and-outs of how to play every Civilization, steam user Zigzagzigal gives a quick summary here. Scroll all the way to the bottom to "other guides" and you will find his more specific guides on each Civilization. I would strongly recommend keeping this in the background to refer to if you are ever stuck on something specific about the Civ you are playing.
There are two things you need to focus on when choosing a leader: Their "unique ability" and their "unique units"/"unique buildings"/"unique improvements". These can be identified as the text next to the "COUNTRY - LEADER" and the circular icons near it. Unique abilities give a lot of insight into how you're going to want to play. For example, America in the screenshot has "Manifest Destiny" which encourages early exploration. Germany's "Furor Teutonicus" encourages defeating barbarians to increase the size of your military. These abilities are often crucial to what victory condition you go for, what types of units & buildings you want to produce, and what social policies you want to adopt. If you go with a random leader, don't worry. You will have the opportunity to review your Unique Ability.
As for the other Uniques, I won't go over buildings (too specific) and I will briefly go over the rare "Unique Improvements". Hovering over the Unique Icon will give you a description of what it requires to be built. For UI's specifically, you are ONLY able to build them on certain tiles. What this means, is that if you are the Dutch for example, you do NOT want to get rid of marshes as they will be future spots for Polders. For Brazil, you want to strongly avoid chopping down Jungle as well. This concept can even be extended to abilities, where Civs such as Morocco encourage that you settle in Desert area, a typically undesirable location.
Now onto unique units: Unique Units are often the brief period of time where your military will have an advantage over others. I would STRONGLY recommend you seek out using them, even if you are not going for a domination victory. However, most unique units require specific resources: mounted units often require horses, sword units often require iron and any unit that looks like a vehicle often requires oil (though, oil-requiring units should not influence your early game too much). What does this mean? It means that wherever you settle, a very critical priority will be access to these resources. How much of these resources you need will also influence what social policies you acquire as well. Your Civ's playstyle will often revolve around the uniques they possess, and very rarely are there Civs who are more "generalist": each Civ often has one or two victories in mind.
So TLDR, make sure to read about all the uniques your Civilization has, and attempt to go for a victory that seems to best use those.