Intel and Nvidia is possible for $700...AMD/Radeon will just give you a lot more for your money.
Before all the PCPartPickers start storming this thread, here are some general ideas:
Are you building a 700 bucks pc to last as long as possible? Or are you building a 700 bucks base to upgrade within 12 months for say...another 700 bucks?
This question will shape the build.
What games do you play? Do you need 4 cores or are you playing lol and cs go...dual core is more than enough. Dragon Age or Far Cry 4? You need 4 cores.
700 bucks for the box alone? Do you need an OS? Do you have a decent monitor and peripherals?
These are question designed to give you ideas of where to go with your build...now let all the pcpartpicker people come and do their work for you...ADIOS!