Charlotte’s damage is heavily concentrated on her NP, which means she wants to be paired with servants who can enable that NP, which generally means Tamamo and somebody else. Any other battery support will do fine in the third slot, whether that’s Waver, Merlin, Jinako, Lanling, or Hans. Lanling and Hans are slightly weaker picks here due to their focuses on crit damage, but in Lanling’s case it does effectively free him to use his battery on Charlotte since his own crit-related buffs would largely be going to waste and thus don’t need to be enabled. Post-buff Bride also has potential value as a support partner, as she can help Charlotte NP repeatedly (and/or immediately) while also pushing damage.
CEs that push Charlotte’s NP damage and/or NP gain are going to be valuable here for obvious reasons. I’m pretty much always a fan of Painting Summer on Arts servants, as it helps them get going faster and NP more often. In Charlotte’s case it patches up her Arts cards and brings her NP gain more in line with the norm for her deck.