What types of Servants for clearing Babylonia?

Berserker

Most of the time I favored st np in the harder fights. A lot of lancer and rider enemies. A lot of boss fights are neutral to everyone, so you have some flexibility. One boss can't be hurt by good servant, half damage from balanced and evil, full damage from other alignment (Bride, mad, summer) so Herc with bond ce. A couple of servants who can dish out instant death is great for one of the last fights (cu chulainn was inconsistent, shiki and guest worked better).

Strong sabers, some good aoe servants, jack the ripper.

Lot of lancer enemies and lots of riders.

Having AOE and ST assassins are both useful (there's quite a few dragon bosses in the main quests). I'm not too sure if anyone else would recommend this but I felt that having a strong ST lancer would have also been useful especially in defeating Ishtar and annoying archer enemies in some of the nodes (as I don't have any strong lancers). And I agree with all the other comments: berserkers (ST, preferably), strong sabers (AOE and ST), etc.

For the Quetzalcoatl boss fight, she takes 0 damage from good servants and half damage from evil and balanced servants. So you could go either with Jack (although Cleo works as well if you don't have Jack)or Herc (with bond CE); I'm not too sure if Nero Bride or any of the summer servants would work (as I haven't used either for any of the Babylonia (or previous) nodes though, imo, I wouldn't recommend them).

My question to you is, what is your servant pool? Anyway, you need a lot sabers and riders for this singularity. AoE is very helpful since the mobs will have a lot of health.

Tiamet: 9.1/9.2, build a sustain team. For these fights, you gain NP quick. I would recommend Merlin for the second fight.
Ishtar: 3.2, use an AoE lancer like Jalter lily. 7.3, use ST lancer. 10.3, find someone with AoE (like Tesla) to wipe out the sabers and use ST lancer.
Ereshkigal: unless you have atlas uniform, use a crit saber like Lancelot. 2030 CE is very helpful for gaining artificial stars. She has NP seal and skill seal which is pretty annoying.
Gorgon: any ST servant will do. You gain NP quick.
Kingu (Avenger): any ST servant and Merlin. abuse his NP and invincibility.
I'm not going to explain Quetz and Ushi since they seem to be explained a lot throughout this site.

My Recommendation:-
Mob Enemy:-
Lancer Mob - Siegfried. I'm sorry but he shine here. enemy is dragon lancer. I'm really sorry I meant the mob is dragon with lancer class and the best servant to kill dragon lancer is Siegfried. I'm so sorry

Lancer Mob - Lahmu. they usually have around 100++ hp so bring single target saber/berserker. for saber I prefer Nero Bride or Okita

Rider Mob - there are two type. the dog one have rather high death rate so shiki is best. another is wyvern. recommendation is Shiki, Scathach, AOE assassins

Beast Mob(only 1 fight against 11 enemy) - Bel Lahmu. these thing have high death rate. so team of Old Man Hassan, Void Shiki and OG shiki will do the job done.

Saber Mob - Bel Lahmu. high hp around 100k++. bring single target archer

there's few mix mob battle so berserker is best for those

Boss :-

Enkidu(lancer) - Single target saber is best
Kingu (Avenger) - I bought my old favourite team, Vlad, Tamamo, Waver
Gorgon - Same team as above
Quelzacoalt - Hercules is really the strongest(Basaka wa tsuyoi ne)
Ushi - 1) Saber/Berserker is best since got 2 lancer lahmu accompany her. 2) fight vs 6 ushi. 2 AOE saber + 2 waver is the best option. 3) anyone will do. just bring your strongest servant. she is classless.

Tiamat :- 1) for first fight Merlin will come as support so any buster servant have best advantage but Martha(Ruler) and Scathach is best as they have anti divine skill. 2) 2nd fight, as above but minus Merlin. I would recommended bring debuff servant as Tiamat have several annoying debuff. Her NP also dispel buff