Graphics APIs and making graphical based games

Hello!
I have been looking all around the Internet today trying to find out how to use a graphics API. I have looked up openGL, DirectX, SFML, and Allegro and have not really come up with what I was looking for. I was hoping to find out how to use one of these. I wanted to make a small, short game kind of like Super Mario Bros. I am relatively new to C++ and programming in general but if feel that if I can get a feel for an API I could focus my learning of C++ more in this direction. If anyone can give me a good idea of how to use one of these or direct me to a good tutorial or even tell me how to set up the API with a compiler this would be greatly appreciated. Also if in your opinion I should just stick to basic console programs for now, I would like the input. thank you!
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Go through these tutorials before deciding the SFML isn't what you are looking for:

http://www.sfml-dev.org/tutorials/1.6/graphics-window.php
http://www.sfml-dev.org/tutorials/1.6/graphics-sprite.php
http://www.sfml-dev.org/tutorials/1.6/graphics-shape.php
http://www.sfml-dev.org/tutorials/1.6/graphics-views.php

It's actually really useful for a 2d game like Mario. Once you've got it set up and linked, it's pretty easy to use.
I do agree that SFML is a very good API to choose for 2D game design (and is more C++ focused).

However I started out with SDL and have always been happy with how it handles, if you aren't happy with how SFML handles I suggest you check out the tutorials here quickly and see what you think. (Just throwing out other options here).
http://lazyfoo.net/SDL_tutorials/index.php
Alright thank you for the input...so, I have got the SFML SDK downloaded, and I tried the Clock program they have for a demo on their Tutorial - Getting started - SFML and Visual Studio page, and I have copied the lib files and the SFML include folder, I wrote out the program and it compiled fine after I set the linker to include the SFML system files. Now this part I don't really understand, right under that part of the page is says if it is linked against the dynamic version of the library then don't forget to copy the corresponding DDLs to you executable's directory. So when I run it it crashes and gives me the message The program can't start because sfml-system.dll is missing from your computer. Try reinstalling the program to fix this problem. What exactly is the executable's directory? I'm sorry if this seems trivial and like I should know this, but I am completely self taught so it might not be the most thorough knowledge and would i just look in SFML/System and copy and paste a file or is this a like of code I need to know? Thank you for you help!
In your SFML folder there must be some DLLs named like that (do a fast search). Copy them in your project directory.
Where is the project directory?
It is the place where your .cpp, .h and .exe files are. Look at the Documents/Visual Studio (Your Version)/Projects directory.
Thank you so much for your help everyone!!
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