Are you using metal needles?
I started out on metal needles, and, like you, was very frustrated with how uneven my stitches were. Then, I tried bamboo needles. Although they're a bit more expensive, the end result was well worth the cost--they helped even out my tension and made my stitches very uniform.
So if you opt to buy some bigger needles, I would recommend looking for bamboo ones. The Clover brand is nice, and Hobby Lobby, Jo-ann's and Micheal's almost always have sizes 7-9 in this brand. If you can't find them in straight needles, try circulars, which are multi-functional in that you can use them to knit a circle or for flat knitting (which is what you're doing).