There really isn't a "best" way. Here are three common methods (which have nothing to do with Spine):
1) If it will work for your game, the simplest method is just axis-aligned bounding boxes. (Exactly what you suggested.)
2) You can use several rectangles (or circles, which are much faster) to make the collision shapes, and test those.
3) Finally, you could create a collision polygon for each character, and use the separating axis theorem to find out if they are colliding. I wrote a bit about this method a long time ago here: http://thirdpartyninjas.com/blog/2010/0 ... on-update/ (Read the linked references. They do a much better job explaining it than my code would.)
Unless you're planning something pretty complicated, one of those should be perfect for what you need.