Classes and races are both the most confusing and most important aspects of Teamfight Tactics. So let's get this straight as easy as we can.
Keep in mind that the game is constantly evolving. Just because the Demons are a pretty mediocre class at the moment does not mean that they will remain the same in the next patch. But even if the balance changes dramatically, the races and classes themselves will basically be the same.
Classes
Elementalists
An Elementalist's bonus is to summon a giant stone elemental to protect your team. This class is excellent because it provides the three best units in the game: Brand, Anivia, and Kennen.
Swivels
Heroes like Gnar, Shivanna, Swain and Nidalee are not very good until they transform (Eliza is always good). But after changing the form, the class bonus doubles the unit's health. This will ensure that your new Mega Gnar or Demon Swain does some damage before being knocked off the field.
Sorcerers
The sorcerer increases the arena points of your entire team and will be our first class with a reservation. Early on, your Warlocks like Kassadin, Lulu, and Ari are not particularly effective. Even champions like Morgana and Veigar won't win you a round. But once you get an expensive hero like Aurelion Sol or Karthus, you can back them up with the damage of the weaker Warlock and watch your enemies melt away from the damage.
Knights
If you are not brave and become a full-fledged Assassin, you will need several tank units. The Knight's bonus makes tanks even more powerful, increasing their armor.
The killers
Assassins are very powerful: they are in the back line and kill enemy units on the sly. Hitting multiple assassins at the same time increases their already high critical damage. The Assassin's goal should always be to kill a unit from behind before he casts his spell.
The Assassin Bonus helps make this a reality. Heroes like Rengar, Katarina, and Pike can work together to help the team gain the Wildlings, Imperials or Pirates bonus.
Screamers
Like the Knights, the Screamers have many cheap, powerful units designed to fight off a wave of enemies. Bonus gives heroes this class extra health, which is always good. And with such objectsLike Vramog's Armor or Giant's Belt, Screamer's health can get out of hand pretty quickly. But unit selection is what lowers the score of Screamers over Knights. The knights have five good units and one mediocre one. The Screamers have three good heroes, one mediocre (Rek'Sai) and one pretty terrible hero (sorry Blitzcrank).
Rangers
Attack speed is a very powerful tool in Teamfight Tactics, so some units are very difficult to fight with. All Rangers are good, and Wayne and Kindred are the best. They focus on dealing damage with auto attacks, and when you combine them, they increase attack speed by ten times.
Arrows
The shooter is our next big class with a caveat. Lucian, Graves, and Miss Fortune are all great, and dealing extra damage to a random unit is a great bonus. However, typing four shooters into a team will almost always be a mistake. It's not that damaging all units is bad; the point is that you put rather useless units in your team, such as Tristana and Kanplan, that kill the class bonus for four heroes.
Guardians
The Guardians have a bonus that is, in theory, pretty good. You make a unit of this class a tank and add bonus protection to all nearby heroes. But the bonus stops being useful when you start learning about units in a class. Leona is a great champion, but she can't get the bonus alone. First you need Braum on the team, and Braum is bad. Sorry, Keepers.
Blade masters
The Blade Master is the hardest class in the rankings. It has two of the best units in the game - Draven and Yasuo. But Aatrox, Gangplank and Fiora are very bad heroes. The extra attack bonus isn't worth adding bad champions to your team. And even if Shen is very good, he has no synergy with Yasuo or Draven.
Races
Phantoms
With the bonus of this class, you kill an enemy unit at the beginning of each round. Not to mention, all three Phantoms are very good champions.
Glacial
The bonus of this class stops the enemy for a few seconds, which is very good. Plus, all class champions are usable except for Braum.
Exiles
At the moment it is only Yasuo, one of the most powerful units in the game. All you have to do is put him aside and he will double his health. Quite simple, extremely powerful.
Wild
Heroes of this class increase their attack speed over time: the faster you attack, the faster you gain mana and deal damage.
Aristocrats
There is a very good bonus here, which just makes one random hero on your team invulnerable. But there are only three good heroes in this class - Garen, Vane and Lucian, while they have no synergy with each other.
Imperials
Great Double Damage bonus and great units, but it depends on the randomness until you hit the full set.
Pirates
Pirates are weird because their bonus doesn't do you any good in combat - it just gives you tons of bonus gold. But it will support your economy, which is pretty good. The only problem is that you have to use the Gangplank, which is no good for anything.
Ninja
Great units, but limited use. One ninja or four ninjas increase the damage of a class, but by the time you get all four champions, you will most likely already have a good command structure. You have to make a very dramatic mid-game shift to replace three of your heroes with ninjas. You can bet on farming and it will either pay off or you can lose very quickly.
Dragons
The Dragon bonus is actually pretty good, as it makes Shivanna and Aurelion Sol immune to magic damage. Both of these champions are great on their own, so why are dragons so far on the list? Well, they don't have a very good synergy. If you have Shivanna, you need two Changer class heroes, and if you have Sol, you need two Warlocks. This gives you six units already, which pushes to the fact that only two of them will be immune to magic.
Abyss
Quite an overwhelming class on all fronts. You need three of these units for your entire team to ignore 50 percent of the enemy's armor. This can be great against Noble or Guardian teams. The problem is that you have to use three Void heroes, while only two of them are decent (Ka'Zix and Cho'Gath) and the rest are just bad.
Demons
Demons have a passive mana burn that can be interesting, but rarely really needed. All demons except Brand and Swain are mediocre or bad.
Yordle
Yordle and Demons are classes with the worst collection of units, but Yordle has a slightly better bonus: with its help your heroes will dodge attacks. However, to get it, you need three champions of this class, which will immediately worsen your team significantly. It's not worth it.
Robots
Robots start with 100% mana. But now there is only one robot in the game, Blitzcrank, and it sucks. So this is a pretty bad bonus.
