I would be interested to find out with what class each of us is the most effective. I can play all classes successfully, but I'm better at playing infiltrator and engineer than other classes (with Engineer on top).
An interesting question. For me, a lot depends on my planned build, and the build progression. Some classes/builds are more effective from rank 1, while others take time while you level up and acquire some upgrades. For me personally:
1. Barring some sort of minimalist Cloak/Adrenaline Rush build, Soldier and Infiltrator are 1 and 2, or even 1a and 1b. I feel this is due to how the Infiltrator and Soldier rely heavily on Adrenaline Rush and Cloak. Adrenaline Rush slows down time and adds weapon damage, while Tactical Cloak turns you invisible--dropping all enemy aggro--and adds damage (or does the damage start at rank 2? I forget). This is good for tactical positioning, either offensively or defensively, and for adding some extra weapon damage.
Even starting on level 1 for the first time, you can gain a level after Lazarus Station for rank 2 Disruptor Ammo, then another level after Freedom's Progress for rank 1 Incendiary Ammo. That is enough for Mordin's Recruitment Mission and then you can spend your time levelling up your passive and Adrenaline Rush.
Infiltrator, same thing, instead you can start on your passive immediately for some sniper time dilation.
2. I would actually put the Adept next. For me personally, on the typical Adept build (Warp, Throw, Singularity, Pull), the Adept does not become effective until rank 4, when I can put at least one point into my main powers.
If you start at level 1, you are stuck with just Singularity and Warp until level 3 when you can unlock Pull or Throw. Effective with Warp-bombs to be sure, but you lack the full effectiveness of the class at level until then.
When compared to tech classes, Adept also kind of gets shafted a bit with respect to upgrades, in that you cannot get your biotic duration or biotic cooldown upgrades until after Horizon.
3. I would probably put the Engineer slightly behind the Adept, even though the Engineer is my favorite class, and on the surface it would seem that the Engineer is more effective early than the Adept.
Engineer has the same issue as the Adept in that it relies on more than just the class passive to be effective, and requires minimum level 3 to start become more versatile.
The good thing about the Engineer is that Overload, Incinerate, and Cryo Blast all start with a radius. Compare this to the Adept where Pull and Throw need rank 4 to get a radius, and Warp never has a radius. That being said, 1.5m radius does not seem to hit more than one enemy all that often, making that radius kind of pointless. This means you need to get these powers to rank 4 if you want to increase the chances that it hits multiple enemies.
Engineer also has more powers with longer cooldowns than the Adept.
Cyro Blast does about the same job as Pull--disable enemies, increase damage and force to enemies--except it has a longer cooldown, it takes longer to freeze than to pull, and it does not pull enemies out of cover rather frozen enemies tend to fall behind cover. Also, Pull can be comboed with Throw and Warp (which the Adept also has), whereas Cryo Blast can only be comboed with Throw (which requires a squadmate).
The Engineer can get the Tech Duration upgrade pre-Horizon (Citadel store, Archangel recruit). You can only get the Tech Cooldown upgrade pre-Horizon with DLC (Kasumi/Stolen Memory DLC); without DLC you can only get the Tech Cooldown on the Disabled Collector Ship or Tali's loyalty mission, whichever comes first.
4. Not sure where I would slot Vanguard and Sentinel. I think I would slot Vanguard next, then Sentinel last.
Vanguard requires a whole new mindset and requires some more careful execution early as you level up Charge. But if you get the hang of it, then it becomes easier to play the more you play it, although you will still probably die a lot. Heavy Charge helps (I took Area Charge once for a playthrough; never again).
Sentinel is in a really weird spot. If you want to play as a caster-type then you have a few choices, none of them really all that good compared to the Adept or Engineer which can do the same with bonus powers + more efficient signature powers for casting. If you want to play as an Assault Sentinel, then you need to level up both your passive and Tech Armor to rank 4, which can take a lot of time if you start at rank 1. Plus Assault Sentinels work better with shotguns, meaning you need that bonus weapon from the Collector Ship.
As mentioned earlier, having DLC helps to get that Tech Cooldown upgrade as soon as possible.