Right now you will see every mistake because you are working so close to the source. Trust me, when the top is turned into a sandwich and the sandwich is quilted, you will not notice the mistakes as much. Some of the smaller inconsistencies will quilt right out and you won't notice them at all. For the rest, pat yourself on the back because you did it and finished!
As for rulers, I don't know anything about the June T. series. I have a 6.5, 9.5, 12.5, and 15" square because those are the blocks I make the most. (Particularly the 6 and 12 come in handy). I spend the time to square my blocks.
Then I have a 6x24 that I use in conjunction with the largest square ruler to square up my tops. Works fine for me.