I also have a gaming build with the fx 6300 (paired with a gtx 670) and it's a great chip. I have mine OC'd to 4.7GHZ on a H80 and it can play anything I've thrown at it on High / Ultra in 1080p (eg. Planetside 2, with everything on max stays above 30fps except in some of the massive fire fights where it can dip into high 20s, which i find is still playable.)
The only thing I would say about your build is that if you want to leave yourself the option to OC on an aftermarket cooler at a later date, you may want a better motherboard. While the 78LMT-usb3 does have heatsinked VRMs, it only has a 4+1 phase count (http://www.overclock.net/t/946407/amd-motherboards-vrm-info-database). For not much more money you could look at the ASUS M5A97 R2.0 or EVO/PRO, which have beffier 6+2 or 8+2 power delivery, which can help with higher stable OCs.
Also be aware that the 78LMT does not support crossfire, haveing only 1x PCIe x16 and no x4 or x8 slots and only supports 1333MHZ RAM (http://www.gigabyte.com/products/product-page.aspx?pid=4305#sp).
Otherwise build looks good and balanced, really like the r9 270!
Hope this helps,
Cheers,
Sam.
Facebook
Twitter
Instagram