I notice this post wasn't closed so I'll weigh in with experience I've had ...
I've used Vegas Pro 9, 10 and currently 12, and tried 4, 6, 8 and now 16Gb ram. With my current system I'm using an FX 6300 OC'd to 4.2Ghz, adequate but by no means optimal, and am using Win 7 64 bit. My GPU is a GTX 650 Ti boost SC edition.
Up until a few weeks ago I was using 8 Gb ram. If I had a browser open with several tabs, maybe email open, and a single instance of Veg 12 open, and was editing and then rendering, it would sometimes hit 7Gb usage (monitored with Win 7 Task Mgr>Performance meter) If I had two or three instances of Veg 12 open under the same circumstances and rendered from one instance, then it would often max - as in like 7.9 Gb ram used. And I was experiencing Vegas crashes.
So I upped it to 16Gb a few weeks ago. I'm using GSkill Ripjaws 1600 cl8 4 x 4 sticks in dual channels
http://www.newegg.ca/Product/Product.aspx?Item=N82E16820231445
Now with 16Gb and under the circumstance where I have the browser, email and three instances of Vegas open - rendering from one while the other two have loaded timelines but are idle, I've seen my computer use up to 15.8Gb ram, and I haven't crashed yet.
My projects tend to have several clips comprising the timeline, rather than just a single or couple clips. My render times are generally just under double the amount of the timeline. ie: a 12 min timeline clip renders in approx 22 mins or so. But for renders, as polke45 pointed out, the actual time is more a function of the processor. If I was using an i5 3570k I would expect it would be faster based on benchmarks. (the FX 6300 has other advantages but I don't want to digress)
Vegas render times can also depend on the GPU. Vegas 12 can take advantage of GPU assisted or OpenCL rendering as opposed to processor only. This can cut the render time by up to about a third. In my case, Vegas can't use the GPU assist cause unfortunately Vegas doesn't have GPU assisted support for cards with the Kepler architecture (GTX 6xx and 7xx series cards) but it does for the older Fermi architecture (GTX 4xx and 5xx cards), for reasons that would be another post. And, Vegas offers GPU assist for all sorts of GPU's. The Kepler \ Fermi situation is an anomaly.
For games, I've only played Tom Raider, Bioshock Infinite, and Call Of Duty Modern Warfare 2, all of which ran fine on high to ultra with 8Gb ram and my other mentioned system specs. My upgrade to 16Gb ram was solely a consideration of editing and rendering with effects. That's where the extra ram will make the biggest difference. With my projects open and editing, I can be using consistently 8 to 12Gb or higher. For your gaming footage, if you were adding an effect like twixtor, you will definitely see an advantage with 16Gb. If you are only opening one instance of Vegas, and editing and rendering to 720 or 1080p, with maybe only things like Vegas's transitions, and some audio, then 8 Gb should work just fine.
8Gb of 1600 ram, low latency, is about the sweet spot, and minimum I'd go. But as polke45 also mentioned, if you buy 16Gb of decent ram you can always swap it into your new build. Depends on what your budget allows. If it were me in your situation, I would start with 8 and save the money to invest in the CPU or GPU. Then if it's not working out for you, you can add 8 more in a few weeks or a month or two when the budget allows. Worst case scenario is you lower the graphics on a game, or slightly adjust your vid edits - you won't experience the crashes I was experiencing unless you start opening multiple instances of Vegas with a ton of effects.
So, in sum ....
- render times in Vegas are mainly a function of CPU - and GPU if supported.
- the extra ram will make the biggest difference for editing footage, especially if using effects, or if rendering with something like twixtor.
- my times would not equal your times because I would need to know system specs; the Vegas profile you are rendering to (Main concept AVC \ AAC? Sony AVC \ MVC? or other); type and quality of the footage; the quality, aspect and bitrate you are rendering to. Then I could match that and give you a better idea.
source: five years of working with Vegas in various configurations