Hey sports fans! (People say that, right?)

Basically, i'm trying desperately to improve my playing ability. I seem to be getting there, but slower than i wanted. I think the problem is, i have a knack for things... Most of the time i become pretty good, or play something somewhat difficult with ease. For example, i taught myself to read music and then play Fur Elise all in one evening (not trying to toot my own horn or anything, so sorry if i came across like that), so when i don't get something quickly i get annoyed with myself and tend to give up.

What i'm doing at the minute, in an attempt to improve and be able to play something awesome, is practicing and playing Sweet Child O' Mine over and over until i can do it all without a problem. So far i can play easy-ish songs from start to end like Green Day, Arctic Monkeys, Oasis etc... So this is actually quite a step up for me. What i'm immediately worried about is because of the 'technicality' of the intro, even though it isn't hard for an experienced guitarist, is that i seem to be messing even that up quite often (hitting strings on the way to another string). So i'm still on that bit because i refuse to move on to the next bit until i get this bit spot on. But, the trouble i'm having with this has me worried about the solo, seeing as i know i struggle with sweeps (although i haven't practiced them an aweful lot before).

What i'm really asking is, what is the best way to improve? Is practicing this song over and over until i get it good enough? Or is what why i'm only improving slowly? Should i be practicing individual techniques by themselves before trying to play a song that uses them? (If so, do you have any recommendations of where to learn those?)

What do you guitar experts suggest? :P How did you do it? What do you tell other people to do? etc.

Thanks in advance! Gonna go listen to more songs i can't play in the mean time :P
I'm not insane, i'm not insane.
try a variety of songs, because as a beginner it may not be easy to judge which song is best suited for you to try at any given time. by trying several, you're more likely to find some songs which you will find playable (for fun/confidence building), and some which will challenge you appropriately. playing many different songs will also force you to constantly reevaluate your technique so it can be used in different situations, which is important if you're going to learn on your own.
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Learn music theory, at least the basics anyway... that way you can open up the fretboard and get out of the box positions. Also start with some slow blues, get used to the intervals in the scale, from there you'll find it much easier to play what you hear in your head instead of just letting your hands do what they feel like! Also if you're struggling with songs like Sweet Child, try playing it much slower than the actual track, that way you build up muscle memory and it'll become much easier to play at the proper speed.. Just keep practicing, learn some licks and play along with backing tracks, just make your own stuff up it'll come eventually.
Thanks guys! I've been learning as many full songs as possible, but like i mentioned in the OP they're relatively easy, even their solos.

I'll try what you guys suggested. JNBloomy, what Blues do you suggest? Are there any songs you suggest, or just Blues licks in general?
I'm not insane, i'm not insane.
I started by learning a few B.B King licks and some Clapton licks as well as creating my own licks just to fill in on solos etc... Just find a backing track of youtube and try to play what you hear in your head (knowing the scale positions will help)