I agree with Astryss and her* thoughts above. That said, and in an effort to offer some guidance that will be helpful now, here’s the view from the casual quarter:
Hunters are always viable in pve content. They solo material well due to the presence of your pet. DPS rating for dungeons is always high, and spirit beasts are generally welcome in groups. That said, there are still a LOT of hunters running around, and some groups top out on how many they want to take along. Also, if you’re running group content, make sure you learn how to manage your pet’s Growl ability. I believe this gets automatically disabled in instances now, but you’ll want to be able to control it yourself, to have it on and off when you want it.
Monks may have had their heyday when they were new in MoP, but I still find the class a LOT of fun to play. Windwalker can pump out some impressive damage, and you have nice self-heals via chi spheres. Mistweaver may be my second favorite healer, and Brewmaster (which, admittedly, I haven’t done much with) has been very strong in recent expansions, I believe. If you’re looking for a class that can play all the different roles, monk is a solid choice.
Shaman might score as the most complex of the three class you mentioned. I love Enhancement spec, but you see people moaning about it constantly. I haven’t done very much with Elemental (because I love Enhancement so much …), but I know Restoration is a solid healing spec. Again, if you want flexibility regarding group roles, shaman is fun. That said, people always complain that shaman gets the short end of the stick in every expansion. Be ready for that. I’ve never felt that myself, for what that’s worth.
Other classes not mentioned that you might like to explore:
Priest. Should you ever want a healer, Discipline priest is a HUGE amount of fun! And different from any other healing spec. The dps spec, shadow, tends to be wonky. You never know if it’s going to be OP or useless in any given expansion. But I don’t care. I stay disc and I have a BLAST!
Speaking of BLASTS, fire mage is awfully fun! So is arcane mage (to me, though some folks claim it’s boring …)
Death Knight is one of the proverbially overpowered classes. Blood DK’s are absolute terrors at tanking. More soloing on current content is done on DK tanks than any other spec, I believe!
I hope this is helpful, and I apologize in advance for any spec that didn’t get air time in this post!