Long Overdue Hardware Upgrade (Help)

Stormbane

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Dec 31, 2012
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Hello, everyone. I'm looking to upgrade my hardware, as the title states.
Here is my current build:

PCPartPicker part list
CPU: Intel Core i5-4670K 3.4GHz Quad-Core Processor
CPU Cooler: Cooler Master Hyper 212 EVO 82.9 CFM Sleeve Bearing CPU Cooler
Motherboard: MSI Z87-G45 Gaming ATX LGA1150 Motherboard
Memory: Corsair Vengeance 8GB (2 x 4GB) DDR3-1600 Memory ($58.10 @ Amazon)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive ($58.75 @ Amazon)
Video Card: Gigabyte GeForce GTX 770 2GB WINDFORCE Video Card
Case: Cooler Master Storm Enforcer ATX Mid Tower Case ($101.06 @ Amazon)
Power Supply: SeaSonic 620W 80+ Bronze Certified Fully-Modular ATX Power Supply ($87.05 @ Amazon)
Optical Drive: Asus DRW-24B1ST/BLK/B/AS DVD/CD Writer ($19.92 @ Amazon)
Operating System: Microsoft Windows 7 Home Premium SP1 OEM 64-bit
Wireless Network Adapter: Rosewill RNX-N250PCe PCI-Express x1 802.11b/g/n Wi-Fi Adapter ($21.47 @ Amazon)
Monitor: Asus VG248QE 24.0" 144Hz Monitor
Total: $346.35

I'm looking primarily to upgrade my GPU as well as add another 8GB of RAM. Probably means I'll need a new PSU, right? Taking GPU suggestions, though trying to keep it below $500 max on the GPU alone (aiming for closer to $400). I know my monitor is only 1080 but I may upgrade that as well, but my main concern is the GPU and PSU problem. If it makes a difference, I'm no longer using the Wi-Fi adapter and will remove it when I upgrade. It's included for completeness.
Also, upon getting a new GPU, will there be any bottlenecking with my CPU or anything? Any other compatibility issues I should be aware of? This is my first time updating hardware like this, and I'm really out of the hardware loop, so I don't know what to expect and I'm really hoping I don't need to rebuild completely. Any and all help is appreciated.
Thanks in advance.
 
Solution
If you update to a GTX 1070 you'd be fine - you really don't have to update anything else.

The CPU is still strong and won't hold back a new GPU in any way.

Stormbane

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Dec 31, 2012
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Thanks for the fast reply.
You sure about the PSU? If I recall correctly, at the time of building I was told that the PSU I have was only just strong enough. Some were recommending a 750w. I'm probably wrong. ._.
If you're sure, then that's awesome news. Not going to pick as the answer yet, though. More opinions are welcome.