I would actually highly disagree with this suggestion. There doesn't appear to be any need for you to build a new system, unless you like throwing money away. While it might be a good idea if your entire system were dated, it's clearly not. With the exception of the graphics card, which is underpowered for a gaming system, everything else would be considered pretty high-end. Assuming your Power Supply is 500 Watts and of decent quality, that should be sufficient for almost any graphics card, outside the extreme high-end cards and multi-card setups that you really don't need.
And for that matter, a GTX 780 would arguably be overkill if you're gaming at standard HD resolutions. You should be able to maintain 60 FPS at 1080p with max settings in almost any current game on a card costing half that much. Sure, there are a handful of exceptions like Crysis 3 that might benefit from such a card on their absolute highest 'ultra' settings, but these games still look great on their 'high' settings, and the developers mainly just include these extreme options to keep their game appearing in hardware benchmarks for years to come. For the most part, the details added by ticking a game's settings from 'high' to 'ultra' will be practically unnoticeable while playing the game anyway. If you do find that newer games require more performance in a couple years, you can always use the money you saved not going with an absolute high-end card now to buy a faster and more up to date one then.
As for which card you should get, there are a lot of options depending on how much you're willing to spend. You likely don't need the absolute high-end though, as even an upper mid-range card would be a substantial upgrade over what you currently have. Tom's Hardware tends to have pretty good graphics card reviews, and they put out an article comparing what they consider the best cards for gaming in various price brackets each month, such as this one for May, which are worth checking out...
http://www.tomshardware.com/reviews/gaming-graphics-card-review,3107.html
Someone else mentioned the GTX 760, which would probably be a pretty good option at a reasonable cost, and should have power consumption well within what your existing PSU can provide. For a bit more, you could move up to the Radeon R9 280x or GTX 770 to give you a little more performance headroom, and their power draw under load would likely still be within the capabilities of your PSU. Unless you find that you're experiencing system instability under load, it's probably not worth upgrading the PSU right away. One thing you will likely want to do though, is open your case (preferably with your system powered down) and carefully measure how much physical space there is for a new graphics card in there. Most higher-end cards tend to be longer than their lower-end counterparts, and could potentially not fit in a smaller case. You should be able to find the exact dimensions of any specific card you're looking at online prior to purchasing it. You can also verify what kind of power supply you have while in there.
As for the suggestion for an SSD, while they're great for making general system performance very snappy, they won't likely have much of an impact on gaming performance, aside from reduced load times. An SSD boot drive might not be bad to look into, though. Again, Tom's puts out a list each month for their current SSD recomendations, sorted by capacity...
http://www.tomshardware.com/reviews/ssd-recommendation-benchmark,3269.html
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