bodie, lots of us cut our borders extra long (by 3"-4") to insure that they fit. I will usually cut even more if I am mitering the corners, but since this is your first project, I assume you are just putting your borders on straight. I would cut the border that little big longer than necessary, leave an ample amount at the edge (for straigntening purposes), then sew. Attach the other side in the same way. Then square up the ends.
Next, cut the strips for the other two sides, attaching them in the same manner. Square up the corners. If you have sewn pretty accurately, your quilt top should be square/rectangular, not curvy (relatively speaking). I think it's easier to have a length of fabric that is close to the appropriate length so you are not dealing with huge amounts of fabric under the needle unnecessarily.
Hope this helps. If not, I know that others will give their own tips, too, and you will have enough to select from to help you.
Welcome!