I've had hounds of some sort since I was a kid, coonhounds for a long time, a few beagles, then bear/cat hounds before the ban and now back to beagles.
The best non-deer training you can give the pup imo is to learn how to use the nose. I usually tie my pups out, take part of a hot dog, give them a tiny bit, tie it to a fishing rod and lay a track for them. First part in their site, then around and out of their site, I slice off a little treat to leave in the track, so they are rewarded as they run the track, and then a half a hot dog at the end. Start short and work up to longer tracks with more difficulty, things in the way, up and over, etc. I run the tracks with them on a check cord so I have some control.
Sounds somewhat stupid but I promise you it works and I can't thank the elderly rabbit hunter from my youth that gave me this golden nugget.