Starting off strong in Pokemon Unite Auto Chess is important. You want to build a good win streak to get extra gold and choose the proper units. Not all units are the same, even if they are the same cost.
Thanks to SilentSheepy, for positing this early game condition, which I have been following from 5000-6000 rankings:

This game is situational and you can’t always follow a fixed strategy (since there is randomness), but it helps to choose the proper stuff early game.
Now, let’s discuss the weak, first. I agree that ice doesn’t do much. The debuff to freeze opponents takes too long to activate and your Pokemon will probably perish by then. For dark, early game, Zorua is very bad and Umbreon is better as a tank, so it’s hard to take down units. Rock is also too defensive and you won’t be doing much with it.
For the OK list, I actually really like fairy early on because of the Zacian summon. Mr. Mime and a Jigglypuff can do lots of work early on to keep you alive and I’ve done this while looking for more Psychic Pokemon to transition to later.
For psychic, I personally like Mr. Mime and Fennekin. I almost always try to look for either of those two and two star them for a nice early game advantage.
For electric, Pikachu and Zeraora are the combo you’ll get early on and they do good work, so I agree with that.
For water, I do like playing Water if I have a chance to get Squirtle and two star to Wartortle with the unite disk. Wartortle becomes an incredible tank. With Wartortle, you need damage, so I pair him with Cramorant
Next for fighting, I agree, it can be very strong early on to get Lucario two star or Urshifu. I don’t like Machop though. Urshifu can be an incredible win condition by itself with the proper items.
Next is grass, if you happen to get a bunch of grass, then you should commit to this build so you can get the grass stacks to claim prizes late game. You must start early or you will be claiming your prizes much too late and you could lose by then.
Finally is fire, which is one of my favourite builds. Scorbunny and Fennekin are incredible units by themselves and when I get both together, it feels great. Then I focus on a tank to keep them both alive so they can dish out the damage.
Besides SilentSheepy’s recommendations, below, are some of my favourite 1-2 cost Pokemon that I will build around:

Attackers
- Scorbunny – even 1 star is powerful
- Cramorant – a great 1 cost unit with a disruptive special move on a random unit
- Rowlet – a great 1 cost unit with a special move that splits your normal attack to another unit. This provides a nice area of effect attack
- Mr. Mime – at 2 star with the unite disk, he is able to deal a ton of damage, despite being a tank
- Fennekin – at 2 star and the second skill, she’s insanely powerful

Defenders
- Umbreon – at 2 star with the unite disk, the tanking is insane
- Squirtle – at 2 star, with the second skill, and with the unite disk, Squirtle becomes Wartortle with great tanking ability
Best of luck to you with Pokemon Unite Auto Chess and choose wisely early game!