I played Skyrim from beginning to end on a 570 and an i5-760 @ 4ghz. Only trouble I had running it was when the game was new and had a bug or poor coding that made the CPU run inefficiently and impacted performance in some areas. After a patch was released to fix that, never had a problem running it (@1920x1200), and this after accumulating some 1.6gb in texture mods. I understand others had problems with over 5gb texture mods, but not sure how widespread that was. Again I suspect this to be poor coding in the game that mis-managed vid mem usage and will not likely be encountered in other games. I just cannot fathom how vidmem runs out at 1680x1050 even on a 1250mb card. It may do in this instance, but I dont think I would buy more than a 2gb GPU to run at that res, even if the shitty coding of one game required it. If I was interested in improving the look and visual impact of the game, the first thing I would buy would be a larger monitor, and even prioritize that over a GPU upgrade.
Re ENB mods, I never associated those with much of a performance penalty as they are mostly post-processing and color enhancements. A few with advanced lighting effects may have some impact but nothing major. Not sure how far they've come now since last trying them over a year ago, but I recall I had to tinker a lot with the settings to get them right and even then was never satisfied due to inconsistencies.