Well the only card that could go in your system and keep up with recent games at 1080p at 60fps medium - high but maybe maxed depending on the game would be the GeForce GTX 950 which has a recommended PSU of 350w which is right on the dot for you (see bottom of page for power requirements: http://www.geforce.co.uk/hardware/desktop-gpus/geforce-gtx-950/specifications) but also I would like to add as you can see on the specifications you will require your PSU to have at least one 6pin PCIE power connector which will plug into the top of the PSU to feed the card the power it requires to run correctly.
Just to note it is advised that you have a PSU about 50-100w above the recommended PSU wattage. My build uses about 400-450 watt full load and I have a i5 4460 coupled with a MSI GTX 970 4GB which is powered by a EVGA G2 550 as the GPU requires a 500w PSU.
I would highly recommend the GeForce ASUS GTX 950 2GB Graphics Card:
http://www.amazon.co.uk/Asus-Nvidia-Graphics-Dvi-I-Pci-E/dp/B014GTF0SM/ref=sr_1_4?s=computers&ie=UTF8&qid=1457352483&sr=1-4&keywords=asus+gtx+950
The ASUS GTX 950 only has 2GB of VRAM which is what the GPU uses to store textures and frames, for more information about VRAM see this thread:
http://www.tomshardware.co.uk/forum/308906-33-please-explain-importance-graphics-card. You should be fine though as on high settings I don't see the VRAM go above 2GB but when I max my games the VRAM can go 2.1-3.2GB depending on the game but I do have 4GB so I can handle it.
The ASUS GTX 950 should suit your needs perfectly.
Regards