Classes that can heal and dps are Warden, Healer and Summoner. All three of these classes have been reworked in recent patches. Healers have been updated so that Caster Dps is now viable, and even decent dps. Summoner was changed in the most recent patch, including the addition of a new skill which allows them to make the most of the Determination stat, greatly increasing their damage/healing. And Warden has been reworked, now allowing them the possibility to play as full healers.
Caster Healer is good for dps, not so good at off heals, unless you sacrifice damage. Warden and Summy both have reasonable off heals because they have group heals that they don't have to channel, unlike the Healer. Though if the full healer in your party is also a Summoner, you will be in competition with their group heal as it leaves a debuff on the group that doesn't allow it to be used again for a minute.
It is possible to change class, so you don't have to worry about being stuck on one forever. I would suggest having a run around at low levels on the classes you are interested in, and deciding which you would like to play after trying them out for a bit.
I hope this helps a little