I feel like I wasted alot of time getting pissed off at the poor sound of sub-standard guitars in the beginning, so much so that it kept me from playing sometimes. It's tough keeping junky fiddles in tune and it can wreck the experience for a beginner.
I don't think you're were wrong to start with a GAX...Ibanez guitars are pretty decent (I own a few too). For me, buying a guitar that can stay in tune while you play it (and even when you abuse it a little through extreme trem use) is paramount. If it doesn't sound good, you won't hear yourself as sounding good and it can bring you down. No matter what you buy, make sure you put it through its paces to see if it can stay sounding good after playing it for a bit. You should spend your time playing or practicing, not tuning.