When my first gaming PC was built - I just went to my local PC shop. I just provided them with the specs I wanted and they did everything from there.
But anyway, I think that it's best if you built it yourself. You might have to learn a few things a long the way, but it would be worth it since you'll have good knowledge of what to do in the future if something were to happen.
If you're really considering building/want more in depth answers, I suggest checking out Tomshardware.
I'm glad you mentioned the games you play because those are the games I play. My PC is not high end:
-i54690k
-Gtx 970
(obviously these aren't the only parts in the case)
Cost was around 700 pounds during the time I built it. For those games you mentioned: in vanilla minecraft FPS is 100+; Skyrim maintains 60 fps with mods on ultra graphics; ESO no lag at all at max graphics. These games are on my SSD.
I chose not to build it myself because i'm lazy. But you might not be, so it's up to you.
Add me on steam if you want. xenice.pvp