Meanwhile the great news is now that you have a guitar you like, you really can go a long ways and have a blast without spending much.
I agree with decpest in the sense that it's okay to make mistakes and it's okay if at first all your notes don't ring clear (maybe they're buzzing because your finger is too far back from the fret, or something). You don't want to get hung up and let that stop you. On the other hand, I also think it's quite a good sign that you are really hearing and noticing your sound.
When you know it doesn't sound right and you know how to correct it, I think it's a fine idea to do so. Otherwise you are programing your muscle memory to perform at a lower level than your ears and mind know to be your musical intention. If you practice playing a passage that you have trouble with, and you do it with buzzing, missed or wrong notes, then, without getting bummed out, you need to matter of factly slow it down until you can play it perfectly, and gradually work it up to speed, but never pushing to the point where you're making more than minimal mistakes. If you ignore this, and push yourself so that you find yourself frustratedly repeating the same mistake, then each time you practice, you are building the neural pathways to wire the mistake into your brain/body. The only way to overcome this is to slow down. Then when you think you're going absurdly slow, slow down some more. It's very hard to do in our "faster faster, gotta have it now" culture. View it like a meditation, and it can have the same relaxing, healthy effect.
On the subject of reading music, I'll pass on something from a great teacher I had once. Music reading isn't 1 skill; it's 3. They are: quick recall of the names of the notes on your fretboard, knowing where they are on the staff, and reading rhythm (note values, rest values, and time signature).
There is a lot of memorizing involved but it's not too hard. It's a good idea to map out all the notes on a neck diagram and then use any memory technique you want. I used to quiz myself mentally while doing other things like riding the bus. I'd randomly pick a fret number, and mentally recite the 6 note names found there. If you think of it like a game, it's kind of fun. It sounds like that's the area you need to focus on to get to your goal, if you have to look at your hands a lot. It could also be that you need to spend some time just mapping out scales and learning how the patterns connect, because familiarity with those makes it easier to know what notes you're playing without looking.
Good luck, and sorry if I was a bit long winded.