It depends on whether you're planning on using a longarmer, and whether you're doing something like entering the quilt in a show. For years, I've managed to put borders on by making long strips, then just sewing them on, trimming the strip so that it's even. That's worked well enough for me when I'm hand quilting, FMQ, or using a walking foot.
Then I got a longarm. You really, really notice when the borders aren't accurate. And, good lord, the problems that occur when they aren't. The way to piece them if you're going to a longarmer is to measure various points along the quilt, parallel to the edge that you'll attach the border to. Average that measurement (so if it's 80, 81, and 82, use 81), and cut the strip to that length. Pin the ends, then fold in half and pin the middle, and, if necessary, fold an end to the middle and pin in the middle of that, and repeat with the other end. Then, as you're going, if your machine is stretching the top or the bottom fabric, you can make sure it matches up. Your borders will turn out perfectly, because you're evening it out as you go.
It doesn't matter whether you put the top/bottom borders on first, or the sides - that makes no difference other than in the look.