I appreciate Zardnaar sharing his list, but I think (based only on observation) that he is missing a fundamental point.
The majority (whether it's slight or vast) of players don't choose their class based solely on the concern of "is this is the most powerful class I can play from levels 1-20?"
Put another way, players often have their own idiosyncratic reasons for choosing classes.
Here would be my list for how I choose (and exclude) classes:
1. To start with, I almost always think of a character concept first, and then figure out how I can make the character concept work using the class framework. What class is "close enough" to the idea in my head?
2. For that reason, I usually start with the concept, and then see if I can single-class (either with or without feats) or if I have to multiclass to make the concept work.
3. However, I do have some general rules that I've noticed I tend to follow in terms of picking classes:
A. No bards, obviously.
B. Also, I hate playing spellcasters. The one exception is Warlocks. So in addition to no bards, I'd add no sorcerers and no wizards. I might play a druid or cleric, but probably not.
That's five classes out. Six if you count the artificer, but you shouldn't.
C. From the classes that are left, I have a preference for martials that don't cast spells or have very limited spellcasting. Monks, Rogues, and Fighters.
D. I've never really like any of the Barbarian archetypes presented ... probably a holdover from 1e. So then Ranger and Paladin. And then Barbarian.
And that's it. It's not really about power, it's about preference. If I had to rank the classes, I'd rank them in order:
Monk
Warlock
Fighter/Rogue
Ranger
Paladin
Barbarian
Druid
Cleric
And I don't like playing the other classes. Why? Because I'm me.