For what it's worth, my advice is to ignore spine testers and also tapering jigs.
They're fine if you're buying arrow shafts that have been selected by weight or rough spine already, but if you're using dowels from hardware shops or better still cutting your own timber and turning them into shafts you should be tapering the arrows differently depending on their weight. If you run them all through the same jig you'll end up with a load of different weights due to the natural variances of the timber you're using. You also would need to make different jigs for every different species of wood which is daft.
Forget spine as well for now, because the simplest method is to finish a large set of arrows without spining, shoot them into a target and group them by where they hit. Get a feel for each group's spine by simply flexing them in your hands and after a bit of practice you'll be able to spine future shafts based on what you learn. It's so unimportant if you're not shooting for competition scoring, and all you really need to know is whether the arrow is safe for the bow you're using.
Beech is fine by the way, it's mentioned by Ascham in Toxophilus and works nicely out of pretty much any weight bow. You'll have to experiment with different tapers to suit the stuff you get, but my initial advice would be to go for a 3/8" size and taper the last 8 or 10 inches down to about 11/32 for a 70-90lb bow.
