Glad to hear that you got a guitar mate!
It will reward you over and over again.
I plug into my pc so I control everything within that.
As for what headphones...
It doesn't have to be a specialist pair,if you already have a set that you use for listening to music,they will be just fine.
If not,spend what you can reasonably afford because without spending a LOT of money,most are much of muchness.
I use a pair that cost me £10:00 from Argos.
Simply because it is not about getting a complete sonic spectrum from them like listening to music,it is just so you can hear yourself playing in the night hours