Regarding Arduino Uno - Counter
The Arduino has a total of 20 pins you can use for whatever you want. D0 through D13 are 'digital' and A0 through A5 are 'analog' but all 20 of those pins can be used for general purpose digital input and output (GPIO). 

So lets see you... you want 14 push-buttons so the most straightforward way to do that is to use one pin configured as an input per push-button. There are more 'clever' techniques, but I wouldn't go there as a beginner.

You also want to drive a 7-segment display. Again, the most straightforward way to do that is to use one pin configured as an output per segment. Unfortunately, 7 + 14 = 21 > 20, so you'll be stuck adding additional hardware or doing something 'clever'. You will in any case need to external resistors in a variety of places (i.e. current limiting for LED segments)

So here's what I would do to keep things relatively simple and still fitting on the Arduino's pins. Give each push-button a pin and configure them in software to be inputs with internal pull-ups enabled. That leaves us six pins to generate 7 outputs... 

That's actually far more than you technically need if you exploit persistence of vision (POV) to scan 'render' the display. You just need to multiplex or charlieplex the segments of the display. Alternatively, you can use an analog input to decode which of multiple buttons are pressed as described in this article, but it doesn't work well for multiple buttons being pressed at once.

Another option is 'get a bigger arduino' the Mega has something like infinity pins...