Is it a good idea to shoot lets say 3 or more different arrows and go with the most consistant one?
That's one way of doing it, but not a very good one. Choose an arrow based on the quality you want to start with. Choose the arrow spine from the charts, but do not choose one that is anywhere near weak on the charts. To tune for exact spine, you have a couple choices. You can adjust shaft length. Or you can adjust bow draw weight. Choose a tip weight that gives you a high FOC. I'd strive for at least 10% and do not be shy about shooting an even higher FOC.
Shoot your bare shaft by wrapping masking tape where the fletching should be, until it equals the weight of the fletched arrows. If you want to shoot a particular draw weight, start with a very long arrow and shoot from about 15 yards into the target (use a target that will not redirect flight of arrow, like a foam one). If the arrow hits tail left (it should), it is showing a weak spine. At this point, you can start cutting the arrow down, and/or reduce draw weight until you get the arrow hitting with the tail centered. At this point, spine will be exact. Be careful not to cut the arrow shorter than your bow/rest combination can handle. If you start out with a lower quality carbon, I suggest tuning until you get them all shooting a little stiff. Low quality arrows with a wide spine variance, will leave you with some shooting weak and some shooting stiff - not a good formula for success. It is better that they all shoot slightly stiff when using broadheads.
If the tail is hitting very high or low, you need to adjust your nocking point. You can test this more accurately by paper tuning from about 6-8 feet.