Best way for taming animals

[Hrenli]

The problem there is that even the basic Chop uses Initiative Points

Sideswipe doesn't, is quicker and weaker, which is perfect for taming.

Might as well ask while it's on the topic: Will using a weapon improve your damage even if your ua and strength is way higher than your MC?

Yes. At the moment using weapon with MC attacks (even at 1 MC) is superior for damage while UA is superior for building openings. That's why people usually use both.

[Potjeh]

Uppercut + Bloodlust into Sideswipe + Combat Meditation is great for taming, yeah, if you can get those skills. As for axe, unfortunately stone axe doesn't really do more damage than punches. You should be able to get bronze going before you tame, though. Ore is pretty much everywhere.