Depending on your project and medium will determine if you can paint upright or flat. Most of my work is flat because my medium viscosity is pretty thin and drippy. 

 If you paint upright with that sort of paint, you will have drips flowing down the surface. Unless that is your mission, then you will want to keep your painting flat. When working with a thicker, more stable medium, working upright is wonderful. 

You will be able to squarely view your work as you are creating it, conversely, working flat gives you a skewed view of the artwork which sometimes causes distortion of some of your figures or shapes in the painting. So try to work upright as much as you can as a beginning painter. The best tool for doing so is to use an easel.  

There are tons of types on the market, ranging from; portable or studio style easels; wooden or metal; large or small. There are so many choices to choose from. When I am on the go, I will grab one of my portable/pocket easels which easily fits into a backpack or art bag. On the go equipment is an awesome addition to your art supply.