You need to find, buy or craft skill books to learn new skills.
You can invest in multiple skill categories, within reason. After act 1 you can easily respec, so can adjust if you end up spreading your skill points too thin, or boost something you end up not using.

The initial class choice only determines the starting skills, equipment and attribute/skill/talent point distribution. You can adjust builds after that however you wish, or if you have not progressed very far, reload the auto save before recruiting the Red Prince and choose a different starting preset. The other companions are nearby, as well, so you could replace him, if you wish.