Yes the Xeon would be ideal; they provide similar performance to i7's whilst being relative cheaper. As mentioned however they have no integrated graphics and you'll need your own GPU; which is by no means an issue for gaming (as you should have your own dedicated GPU).
Yes the Xeon E3-1230v3 (or whichever you desire to purchase, preferably higher) is definitely worthwhile over the i5 and even the i7 too if you're on a budget. You won't be disappointed with the Xeon, I even have one.
In your case if the Xeon doesn't cost too much more than the i5, I would go with the Xeon. Otherwise it's completely your call.
All the best.