Well it depends on which MB you get and if you upgrade the case or not. It sounds like you really need a new PSU. Now some people will replace the fans on their PSU's, but I suspect it wouldn't be worth it for yours, and that you wouldn't feel comfortable doing it. I assume your PSU is out of warranty.
This is probably what you should do:
PCPartPicker part list /
Price breakdown by merchant
CPU: Intel Core i3-6100 3.7GHz Dual-Core Processor ($110.99 @ SuperBiiz)
Motherboard: Gigabyte G1.Sniper B7 ATX LGA1151 Motherboard ($82.98 @ Newegg)
Memory: Crucial 8GB (2 x 4GB) DDR4-2133 Memory ($30.98 @ Newegg)
Case: Phanteks Enthoo Pro M ATX Mid Tower Case ($54.99 @ Newegg)
Power Supply: Antec High Current Gamer 620W 80+ Bronze Certified Semi-Modular ATX Power Supply ($59.99 @ Newegg)
Total: $339.93
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2016-06-09 18:55 EDT-0400
The i3 6100 would be a significant upgrade over the i3 530, but you are GPU limited, so I'm not sure you will realize any real benefit. When you are ready for a AMD RX 480 or similar, you would likely only have mild bottlenecking on certain games with the i3. With your current GPU, you won't get any added benefit from the i5 over the i3 for gaming. With the Skylake MB, you'll be able to upgrade all the way up to an i7 in the future if you want. You really need to upgrade everything.