It depends. If it is a special pattern that may be hard to piece, I will cut the length of fabric. If it is a pattern that can easily be pieced, I cut across and sew the short pieces together.

What you are saying is that when you cut the length off (and you need to do that first) then you need to be careful that you have enough left over for the piecing of the blocks? Did I understand that right? You have to plan how much you need for piecing and how much you will lose due to the border strip being cut off. It's that math thing again.

If your top is 45 X 45 you will either have to have a seam or corner blocks. You can add the 45 inches to the two sides but when you cut for the other sides they have to go over the 2 sashes you've already sewed on. Does that make sense? I usually plan to cut the borders without seams but I do like the look of a block from the quilt in the border in some instances. This can also be used if you don't have enough fabric to cut without seams, make a deliberate insertion in the borders as an added touch.

I prefer to cut my borders lengthwise. Less chance of having wavy borders.

Same for me and if I have to piece the fabric then I do it on the diagonal!

I prefer to cut borders from the length of the fabric. It seems to prevent wavy borders. I will piece a border, however, if I love the fabric and don't have enough for the other method.

It depends. I use a cornerstone block sometimes if it will allow me to get by without piecing the rest of the border.