I would just research WHM and SCH and see which one suits you better. WHM is better AE heals and has the most direct/straight forward healing of all the classes. SCH is better single target healing and uses a lot of damage mitigation rather than heals, and is also a pet class.

Other things to factor in, SCH and WHM compliment each other almost perfectly. So if you have any friends you raid with regularly, pick the healer opposite of them. If you do a lot of pugging, then WHM is the safe choice.

AST is in a really bad spot atm and I honestly couldn't recommend anyone pick it up unless they really enjoy its playstyle (which I personally do enjoy a lot). However, it is almost certainly going to be buffed in 3.1. By how much is unknown though.