So i manage to get arthuria archer in that summer banner but idk a good support for her
Tamamo (Caster) will definitely be your first choice, the extra arts effectiveness on her third skill, plus the NP gain and the skill cooldown reduction on her NP, fits in perfectly with Summer Saber's gameplan of NP spamming. Waver fits in as usual to top her NP gauge off when she needs it, Hans also works well since Arturia will be able to make good use of the stars.
Squirtle actually doesn't really need support and is very self-sufficient and actually able to solo content due to this.
Because of this fact she can use multiple support setups for multiple comps. The most facerollish of these would be using her with Tamamo no mae and waver in the ultimate stall team (3 different sources of charge drain which is op). Another version is an arts crit team with Squirtle, waver and Emiya assassin (or even fuuma). She isn't the best crit dps with no talents to support her crits like Chloe has but she does decently enough and the crits do help with her primary np spamming role.
Most compatible:
Tamamo no Mae
Waver
Nero Bride
Caster Gilgamesh (Later on after Babylonia releases)
Alternatives (and budgets):
Mashu
Helena
Mozart (for burst)
Hans
Pretty much what has been said already. Tamamo-no-mae is the ideal support with her arts up, but really, Archertoria is a very self-sufficient servant who doesn't need a lot of support.
If anything, I'd say throw a crit star generator like Emiya (assassin) or Kotarou in there so she can take advantage of her independent action; so she's still doing ungodly amounts of damage even when not using her NP.
