Hi there
Well for starters you're totally right about that AMD Phenom II x6 being more than enough, with the emphasis on
more.
All current games use a maximum of 4 CPU cores (most use 3 in fact, with a few using the 4th for sound.)
The important thing to note about your CPU is the specifics... That line of CPU employs a technology called "Turbo Core Tech" which basically switches off 3/6 cores during gaming, and uses their power to "overclock" (fuel more power into) the remaining 3 that still run. CPUs all have clock speeds (which is how fast they process.) Overclocking is adding more speed to that clock. So whilst that CPU will have fast clock speeds (depending on which model AMD Phenom II x6 you buy), it'll have only 3 cores working whilst turbo tech is enabled (you can disable it, but then your clock speeds will fall.)
Now we can compare this to the Intel i5 2500k. I think the 2500k is currently the best budget gaming CPU, as for gaming it is pretty much the best CPU Intel can provide you, but it retails at a ridiculously low price for what you get. The 2500k is a 4 core CPU (perfect for gaming) and has clock speeds of 3.3Ghz in standard mode, but a turbo boost which activates during gaming to take the speeds up to 3.7GHz. Now those clock speeds are exactly the same as the best AMD Phenom II x6 but you also get to keep that 4th core on the Intel (which admittedly won't necessarily be used now in all games, but will be used in future releases, and will at least benefit you somewhat.)
What I'm trying to say is that the Intel is the better choice for you. It may be slightly more expensive , but it is incredibly cheap for what you get.
Look at this benchmark for info regarding the AMD Phenom II x6 vs the Intel i5 2500k.
http://www.anandtech.com/bench/Product/288?vs=146
As you can see, in most gaming tests, the 2500k beat the AMD PHenom II x6.
It is also important to note that around October(ish), AMD is going to release its latest CPU lineup, and therefore AMD prices will likely drop. This will probably also cause Intel CPU prices to drop to stay competitive, so if you can wait for a little while longer you may be able to get a cheaper PC (but yes, I realise this is right about the time that Skyrim comes out, so may not be possible.)
So, on balance:
Both CPUs will perform well, especially for gaming. However, if you really want to get the absolute best deal price/performance wise, the Intel CPU will be better for you.
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The 6450 would play Skyrim on very low-low settings with low FPS.
The 6670 would play Skyrim on low settings with medium FPS.
As Jord suggested, you should probably consider something such as a 560 Ti, or a GTX 570. The 580 would be great if you could afford it, but is very expensive, and you can get better performance for less money by getting two 560 Ti's and putting them both in your rig in SLI (providing you have the appropriate SLI ready components.)
Either the 560Ti or the 570 would meet your needs well, and you could later install another of whatever you got in SLI for about 1.9x performance increase compared to the original single card.
It's important to note that if you buy a PC from Dell (who will crank the price up compared to either building your own or visiting a company who build PCs for you), switching any parts (or even opening the case) will most probably invalidate any and all warranty you buy from them.
I do suggest you look elsewhere for a company that can build a computer for you (I'm not familiar with American prebuilt companies as I live in the UK) or a more technical savvy friend who will help you build your own.
Anyway, I'm sorry if I've confused you further, but I do think it's important to make sure you're in the know about every choice you're considering
If you have any questions ask away and either myself or someone else will surely answer them for you
Good luck
-Nih