Ok, I've read many guides on re-stringing my electric guitar... Even the one on this forum, but my question is... As I near the part where I have to put the string through the tuning peg, should I wind it round the peg first, or go through the peg then wind it through? This seems to be the part many guides miss out, instead just saying "wind it through then tighten"

Some people wind it around the peg first, i personally just put in the peg and then turn the knob.
Depends on what kind of bridge/tuners you have. Vintage trem, hardtail, or non locking tuners etc. you should wind around the peg first. If you have any kind of locking tuners, floyd rose, etc. you can just go straight through with minimal slack in the string.
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Custom Fender 62' Reissue Strat
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I just put it in and twist the knob.

That's what SHE said!

You can check out the link in my sig that explains a lot of guitar how-to's.

This link here will get you straight to stringing the guitar! Specifically the part with the peg, which can be hard for the first-timer. https://www.ultimate-guitar.com/forum/showpost.php?p=9502116&postcount=2
Ultimate Guitar Set Up Q&A Thread─┤
I always put the string through, loop once, then put it through the hole a second time, tighten the string. After that wrap the string or cut it away.