Base of Tamer mage is 120 Taming, Lore, Vet. This will give you all the skill based bonus stable slots and get rid of any issues when you level pets. Later you can omit/soul stone off Vet if you want to change the template.
Recommended 110 magery. Never fail gate or mass dispel. Mass dispel will be used when you beat down some pets that need it in order to be tamed.
If you want to explore Fel, or plan to make a character on Siege add Hiding and Resist. It's also helpful if your connection is slow, or to give yourself some margin of protection from dying. It's a good basic template for an explorer/PvM type on a ridable pet. Downsides, not that flashy and lacking that extra something sometimes.
Discord can be added to a pet now, so really there's not much reason to use points in bard skills unless you find that play style fun.
You'll want to get your book of mastery, and if you get a Level 3 Animal Taming, you'll want to build an armor set that allows you to run the pet healing perk. Also, if you have Taming Mastery on, it will give you more stable slots. High end skill gain also can be done much more easily by repeated casting of Mastery L1 spell and cancelling it.