A 4gb with enough CUDA cores (1500 or more) card would be the recommended minimum for rendering in iray. I have a 980gtx with 4gb and so far haven't ran out of memory for my scene. If you render larger scenes then you will need to go with a card with more memory. The 980TI has 6gb of ram and the Titan X has 12gb. You wouldn't need to build a new computer to use iray; you would need to make sure the motherboard can use the new card (probably it can), the computer has a big enough power supply to handle the card, and the case is big enough for the new card to fit.

You can use cards in the 700 series as well, but he newer cards do better with power consumption so if you have enough power, you can run your current card as the main video card and then dedicate the new one for iray renders only. That's my setup so I can watch videos and web surf on my 580gtx while the renders run on the 980.