Whoever told you that the GTX 670 is better than the GTX 680 doesn't know what they're talking about. When it comes to a price to performance comparison, the GTX 670 is the better value because the 680 does offer better performance but not by much. At stock clocks, the 7970 isn't as fast as a GTX 680. I'm not sure how the factory overclocked Ghz edition cards compare, but the 7970's will definitely perform better than the GTX 680 when overclocked.
I would personally go for a 7970 unless you're going to spend some extra money and get a 4GB GTX 680 and an ultra high resolution monitor in order to utilize the extra VRAM.
When it comes to monitors, you're going to want to look at resolution, contrast ratio, and response time. You might have a preference when it comes to brightness as well. Another thing to look for is whether or not the monitor has an anti-glare coating. Anti-glare coatings can be nice for rooms that have a lot of light pollution, but monitors without the anti-glare coating will look a lot more vibrant and colorful, although they will obviously be more vulnerable to glare issues.
When it comes to response time, you're generally going to want between 2ms and 5ms for gaming. If the response time is too slow, you could have lag-like issues. Brightness is really just your own preference. I personally like brighter screens because I think it makes the colors pop that much more. Contrast ratio is kind of a shit show at this point, because everyone rates contrast ratio with a different standard. Most companies rate contrast by something called a "Dynamic Contrast Ratio." Dynamic contrast ratio is what the display is capable of doing, no questions asked, but standard contrast ratio measures how much contrast a screen can output at one time. Standard contrast ratios are more accurate, and the higher they are the better. Contrast ratio is just the measure of how black your blacks are and how white youre whites are, btw.
Simply put, you want the lowest response time possible, highest contrast ratio possible, best resolution for your graphics card, and brightness and anti glare are personal preferences.
If I had to pick a monitor for your build it would be one of these:
http://www.shopping.hp.com/en_US/home-office/-/products/Accessories/Monitors/LM914AA;pgid=c7twGfjc0ptSRpIq7ZUcoGXQ0000PpVVSUTr;sid=2WfJySfiXXn03HefYh9uQf_t7XsMnBP-HDIhYsrz07xEYp1xG9HKH5RZ?HP-x2301-23-inch-Diagonal-LED-Monitor#pdpspecs
http://www.newegg.com/Product/Product.aspx?Item=N82E16824236153
The HP has no anti-glare protection, and the screen is extremely glossy. It gives you an amazing looking picture as a result, but it is very vulnerable to glare.
The ASUS has anti-glare protection, but it's still a very nice monitor.
Other things to keep in mind is whether or not the monitor has an LED backlight. LED backlights are more of the standard now because they use less power while preventing light bleed. I wouldn't go with a 120hz screen unless you're planning on getting two high end video cards and planning to do some 3D gaming or watching 3D movies.
Another technology to look at are IPS panels. IPS panels have great color accuracy, but they generally have higher response times.
Btw, link me to the ram, and I'll let you know what I think.