Your unevenness could be from lots of things (all of which we all did when first learning!),inaccurate cutting, seams that were not all 1/4", stretching of fabric when assembling or pressing, etc. Unwashed fabric pieces can also shrink inconsistently when steam pressed. As you get more experience you will get better at eliminating these issues.
As for squaring up, if your cutting and 1/4" seams are accurate you should not need to square up. But many quilters square up every block or even sections of a block as they go. I usually check to see if any trimming is needed on each block before sewing into rows or columns.
I agree with Prism99 that once the top is quilted, much of your waviness may not be an issue, especially after it is finished and washed----the natural crinkling that occurs from the shrinking of the cottons and the batting hides a lot of errors!!����