http://www.newegg.com/Product/Product.aspx?Item=N82E16883229496
something like this can handle Skyrim on medium easily, skyrim is more CPU bound than it is GPU bound, and as for mods, if it's just gameplay mods like new animations, gameplay overhauls, NPC overhauls etc, then it shouldn't affect performance
if you want to use graphical mods and enhancements, you'll need a stronger graphics card (and PSU probably), so if you have the patience to upgrade this PC into something stronger then an idea would be to sell the PSU and the graphics card, and get about 50-60 bucks out of it.
Then buy a nice mid-ranged grpahics card like:
http://www.newegg.com/Product/Product.aspx?Item=N82E16814121686
and an okay PSU with enough wattage like:
http://www.amazon.com/dp/B00DGHKK7M/?tag=pcpapi-20
it'll cost a bit more than 750 (even after selling the old graphics and PSU) for the whole thing but you can save up money for the 2nd part, and after it's all done you'll have a PC that can handle Skyrim on high or ultra with a ton of mods like texture enhancements, ENB, parallax mods, etc.