I've always bought calf halters (and yearling and cow and bull halters) at our farm supply store. They're like the one below on the cow - the bottom crosses under the jaw, and doesn't hang down to get hung up on things (Turn Out halter).
http://www.ebay.com/itm/HAMILTON-30D...7151%26ps%3D54
I agree it is better to not leave them on all day, but in certain situations where there is nothing on which they could catch, it would be okay.
I actually start training calves the first week of life, and even the calf halters are too small, so I start with a llama halter.
Before you worry about leading the calf around, the calf needs to learn to give in to the rope. So you tie them up and let them struggle a bit until they discover that giving up and going toward the rope relieves the pressure of the halter behind their ears.
Tie them up for a few minutes the first few times, and increase the time. Just tie them with just a few feet of rope so their legs can't get over the rope.
When they learn to quit fighting the rope, then you can try leading them. Just hold pressure until they learn to give in and follow you.