Not only is it safe, but necessary! I'd hold off on the lunging, though, and make sure you take baby steps that your horse is ready for.
Could someone explain why lunging is bad for young horses? I know it's been mentioned several times, but not why.
I'd start with leading, trailering, desnsitizing, etc. I wouldn't put the bit in for a while, though. The last thing you want is a bad experience! However, if you go slow and you do everything you can go get your horse used to you and working with you, getting him used to the bit will be fine. I got long-reins and taught my horse to give to aids long before I ever got on him. However, I found it worked better to teach giving to pressure on a sidepull, then introducing the bit after he got the idea of what was supposed to happen. Then, I never had to give very much pressure on the bit at all, because he already knew what a tap on the rein and a press with a foot meant, as well as all voice aids.