Buy this:
http://smile.amazon.com/Elgato-Game-Capture-HD60/dp/B00MIQ40JQ/ref=sr_1_1?ie=UTF8&qid=1428712330&sr=8-1&keywords=record+60+fps+games
First, NO. That device is fraking garbage, because it transfers the video over USB 2.0, which doesn't have the bandwidth, and so it very poorly compresses the video first, and you lose a lot of quality.
Second, if you're going to use a capture card, you need a second computer. So you're talking a 2-computer setup. Notice how it says "for PlayStation 4, Xbox One and Xbox 360, or Wii U gameplay", as its captures those consoles "right to your PC or Mac". If you're going to capture a computer with a computer, you need two computers, or else you're doing it wrong.
Third, the better way is to use Open Broadcaster Software to capture Aces High gameplay to your hard drive directly, no capture card needed:
https://obsproject.com Follow the OBS setup guides, and make sure you're running Windows Vista or better and that your GPU fully supports DirectX 10 or better and your drivers are updated. Use Game Capture. If you have a recent Nvidia card, you can use the built-in NVEnc encoder, same as Shadowplay uses, except with OBS you have more configuration options. If you have an Intel CPU, you can use Quicksync encoding with OBS. If you have one of the latest AMD video cards, there may soon be an AMD equivalent to NVEnc available, there's a fork of OBS with it in open alpha testing now.
Fourth, if you do have a second computer you want to do all your encoding tasks on, get a decent capture card (at the same price), not the P.O.S. that Challenge mentioned. (And use it with OBS mentioned above.) Here's the most trouble-free popular capture card on the market:
http://www.amazon.com/Live-Gamer-HD-Lite-Acquisition/dp/B00GLPYA1I . It'll allow you to input 1080p60 and record it at 720p60 or 1080p30, either choice will be far better quality than the Elgato device, or any device that inputs HD video over a USB 2.0 port.
If you want to spend more, you can find capture cards for full 1080p60 input and output, but they require USB 3.0 or a PCIe 4x slot... if they claim to need less, they're pre-compressing the video and you should avoid them for numerous reasons. To see what I use, check my Twitch link in my sig.
As for video editing once you've captured your video to your hard drive, I personally think the best price/features/performance tradeoffs for an
NLE for amateurs like us is still Vegas Movie Studio (HD Platinum version... whatever). There's a 30 day free fully-featured trial on Sony's Vegas site, which will more than likely convince you to buy the full thing, old versions of which are not expensive:
http://www.amazon.com/s/ref=nb_sb_noss_1?url=search-alias%3Delectronics&field-keywords=vegas%20movie%20studio . Get the Platinum version though, as lesser versions I believe have poor output options.
Once you're done in Vegas, save it as an extremely high quality/bitrate "intermediate" file, and then use Handbrake to compress it to something you can upload to YouTube. Be sure to keep YouTube's H.264 encoding recommendations in mind:
https://support.google.com/youtube/answer/1722171This YouTube video tells you an very nicely how to save an intermediate file out of Vegas and then use Handbrake to make it to the final product for upload to YouTube:
https://www.youtube.com/watch?&v=rWMX5lSvEgY