Re: String through bridge or body on a tele?
The 'Real' Tele tone does involve strings-though-body, no doubt about it in my mind. The trade-off is the greater string tension, but if you're after the whole original Tele vibe, the strings need to go through the body. The sound is bigger and fuller in all the desired Tele ways.
Tele's are amazing in that they can be set up in a lot of ways to cover a lot of playing styles, but a few basic things are a must for the original authentic Tele goodness....
Steel bridge plate, 3 brass saddles and the strings-through body are probably the biggest three factors. Some will also say there is a difference between using small springs or rubber tubing for tension on the bridge pickup mounting screws. I'm sure there are other factors as well. But strings-though v's top-loading is a biggie in Tele-land.