Let’s go through this one Servant at a time.
Zerkerlot as a Quick Meme Servant. I’m assuming you mean the Quick NP Looping with Skadi with this. The issue is that his damage isn’t all that amazing. As noted in GP’s SR Ticket Guide, Zerkerlot has limited farming capabilities at NP1. It’s not completely unusable, but to make the most out of Overkill to boost his NP Gain, you’ll need higher damage to reliably trigger Overkill in higher HP enemies like those with 60k health and such.
Nursery Rhyme makes for a decent anti-Assassin farmer with her NP Battery, but she lacks any sort of offensive buff to power her NP and she can’t reliably generate crit stars for her crit game. She’ll work extremely well with CasGil though. Gil’s buffs allow for even Arts cards (which normally have a 0% Star Gen multiplier) to generate a good number of crit stars and his own NP creates a lot of them for Nursery to grab and use. So the two of them make a pretty decent pair.
Tristan has great utility skills with his 1-Time Team-wide Evade and enemy Buff Removal. He’s good against enemies who like to spam Evade, and his upcoming NP upgrade lets him ignore DEF buffs too. However, he does lack in terms of offensive buffs so his overall damage isn’t that good, and his NP Charge seals his NP for one turn so it can’t be used the same turn as the charge.
Out of the three, you’ve only mentioned needing an AoE Berserker. So if it’s out of necessity, go with Zerkerlot. But I would also recommend Tristan because he’s story-locked and cannot spook you unless you roll on a banner where he is featured.