It's hard so say that there's a "best" since they all have pros and cons, but i'm gonna list my favorites and why I prefer them over the other classes and specs
So for Melee DPS I prefer Marauder/Sentinel with the Carnage/Combat spec, because they have an extremely high dps output with a high mobility.
For Ranged DPS I'm gonna go with Mercenary with the IO spec (Innovative Ordinance). This class is my overall favorite DPS class, because of the high range (30 meters to most attacks), high mobility and of course the extremely high DPS. Since they are dual-wielding they have higher dps than their PowerTech counterpart (even though I adore PT too). The rotation is fairly easy too, so this spec would be good for new players as well, whereas i find Mara/Sentinel to be for a bit more experienced because of the rotation and the "glass-cannon" aspect of it.
For Healer I'm definately going with Sage/Sorc, just because it's such an easy rotation mixed with extremely powerful burst healing. I also like Scoundrel/Operative, because they have a bit more mobility than Sage/Sorc, but i'm still gonna go with the force using healers. I am not a big fan of Merc/Commando healing, since they don't have as powerful healing abilities and it's a harder rotation. The upside for Merc/Commando is that they can take more damage due to their heavy armor.
And lastly, Tank; This is tougher since I mostly play healer and dps, but i've had around 3-4 tanks, so I'm gonna try. For tank I'd go with Guardian/Juggernaut, because it's an "in-your-face" kinda tank and can take a lot of damage while relying less on the healer to keep them alive. My second choice is PowerTech/Commando, because as a ranged tank they have better overview of the situation and mob.
That is just my opinion. And as i said there's no such thing as a "best", it all depends on the player, what they enjoy and their playing-style.
P.s I apologize for spelling-errors and mistakes. English isn't my first language.