You can level multiple classes on the same character, so you won't have the same alt problem as in other MMOs. In fact, it's easier to level up multiple classes on the same character than on an alt (because of the 50% exp bonus you get when leveling a class lower leveled than your highest level class). You can still make alts if you want, but it's mostly just for cosmetic purposes or in the rare case that you play so much you cap on dailies and weeklies instantly. There is very little branching of the storyline nor any significant difference between factions in this game. The only question is which class you want to level first.
Paladin and White Mage are both very strong classes now. White Mage is much more of a dps and healer hybrid than any of the other healers now, but their primary role is still healing. In comparison, Astrologian is much more support-based and is less able to do damage on its own.
You seem like a player who likes their utility. In that case, Bard and Red Mage should definitely be considered. Those two classes still feature high damage, and like many DPS classes, are not as durable as a tank, but canbring a large amount of support to the game.
Bard has the most utility of any job you want. You can provide a buff to crit, restore TP and MP, increase maximum HP, increase the healing someone receives, reduce damage, and remove unwanted status effects.
Red Mage is a new job and it is considered a magic dps class. However, it provides a surprising amount of burst healing because of the way their heal scales off INT (also your main stat), and the fact you can effectively cast 2 spells at once. You also get a raise effect at later levels that you can effectively instant cast any time you want, and this makes you a secondary/tertiary healer in most groups. You also have abilities that restore MP and reduce magic damage if you want even more utility.
As for the controller, everyone has their own preference for which works better for them, but there is no big difference in how it works. I will admit however, that healers seem to use the most macros out of any role. So keep that in mind if you're not comfortable making or using them.