Should I get a graphics card?

[CommanderLiamTHX]

I was thinking of building a computer for a family member who pretty much just needs to check her emails and play flash e cards really loud. I was listing all the parts I would get on Newegg to build it, but I came across the graphics card. Because of her basic needs, would this be necessary to buy? The processor is an AMD FX-6300 Vishera. The case I'll be using is here: ENERMAX OSTROG ECA3253-BL Black / Blue SGCC / SECC ATX Mid Tower Computer Case - Newegg.com

 

[PP Mguire]

You're going too overboard for somebody who is doing the most minimal of tasks. All this person needs at most is an i3 4130, and I mean at the most which is stretching it. You could even do this with a 50 dollar Haswell Celeron and a very cheap Asus H81 board.

For a case this is the most "fancy" I would do unless you decide to go mITX which would just be more costly.
Antec NEW SOLUTION SERIES VSK-3000 Black SGCC steel MicroATX Mini Tower Computer Case - Newegg.com

To answer your original question, if you get that FX CPU you'll need to buy a GPU. If you get an i3 it comes with an IGP.