When you start over, once you get to New Tristram, your three followers are hanging out in the corner between the blacksmith and the mayor. You can hire any of the three of them immediately, and they keep all of their armor/weapons/jewelry. However, when you're working your way through the cathedral on your way to kill the skeleton king, you still have to go through Jondar, and there's still a "warrior" who's being held captive by cultists, who turns into the templar when you get his gear out of the chest. So right now, I have the Scoundrel and the Templar following me, but I can't check out the Templar's gear, because he currently exists the way that Leah or Tyreal do when they're following you around.
Once you get Jondar down to almost no health, and he begs the Templar for forgiveness, you go through that little scene where the templar kills Jondar, then the templar gives his speech about how he'll join you on your quest to kill the skeleton king, on the one condition - blah blah - then comes to attention, salutes, and fades away (assuming you don't have the Templar in your party at the time. No idea what happens if you do).
On a completely unrelated note, on normal difficulty I always kind of hated getting a Protection shrine, because it was just a waste of a perfectly good shrine. On Nightmarish, I love them.