upgrading from a8-5600k

[greatmanya]

Currently my specs:
Windows 8.1
A8-5600k 3.9 GHz paired with Thermaltake 2.0 water-cooling
FM2-A75MA-E35
8 GB 1866 Ripjaw
sapphire 6870 1 GB
600 Coolmaster PSU
Screen - 1920 X 1080

Now my question is, if I were to upgrade would it be wise to upgrade the cpu/mobo or just the graphics card or all three components?
I was trying to play Skyrim with 20 different mods on 1980 X 1020 when I noticed a lot of lag and wanted to upgrade for Skyrim and future games.
Basically this will strictly be a gaming pc with some multitasking here and there.
I don't have a high budget so if needed I can upgrade slowly- max $350
I was looking at i5-3470 and fx 8350 but cannot decide which one to get or even if they are worth getting. As for graphics, something like a 270X or 760 gtx.
But I am open to suggestions.
PS I am a Canadian so will be using NCIX.ca or newegg.ca or memory express - wherever I can find a better deal!
Thank you all

 

[RobCrezz]

edit, I would upgrade the CPU/mobo first, graphics later, the 6870 is still not too bad for many games.