The deciding factor is whether or not you feel comfortable assembling the computer yourself. There are half a million online tutorials and it is relatively easy. You shouldn't end up spending over 600$ for a gaming computer just to play Skyrim completely maxed out then, if you want a rig that will keep playing games at highest for at very, very, least a year to come it might go up to 700$ or at worst 1000$ but that is an
extremely high end computer

If you want to buy an already built computer you will spend about 30-70% more and possibly not get everything you wanted.
Over the past two months I pretty much gutted my computer and replaced most of the components for under 500 dollars. The only components that remain are the case, my hard drives, sound card (which I technically don't need since my motherboard has onboard sound) and wireless network card. Motherboard, video card, CPU, memory and power supply are all new.
PSU CORSAIR|750W CMPSU-750TXV2 R......................................................................................$100
VGA POWERCOLOR|AX6850 1GBD5-DH R (Radeon HD6850, included free copy of Deus Ex HR)......$160
MB BIOSTAR|A870 AM3 870 R Motherboard...................................................................................$60
CPU AMD Phenom II X4 955 3.2G AM3 RT Processor......................................................................$120
MEM 2Gx2|WINTEC 3AXH1333C9WS4GK R (2 sticks of 2GB DDR3 1333 memory)...........................$30
Total $470
yep, very nice price quotes

You don't need much over a GTX 260 to play Skyrim at max.. since they didn't add in a 'super euber max' graphics setting anything beyond max doesn't really matter... and the GTX 260 is a 90-110$ graphics card... at most pay 250$ for one and that means you want some serious sh*t, with the way prices for graphics cards drop, anything over that is just wasted money
if you have any sort of quad core you will be fine, ideally you'll have least a 2.6ghz one.
This man's prices are pretty dead on though for low ball-ed, yet solid, hardware for a computer. I found my intel motherboard for 60$ (with mail in rebate) and its a top notch new enough model
I doubt this would max Skyrim, most likely high settings...
I'll double check the graphics card (at 160$ the card
should be fine)
everything else he has is beyond whats necessary to max Skyrim out