What banners/servants should I save up for to help my team comp?

Rolling for Archer Arturia is a good plan, she's a great one. Gil or Ishtar can fill the AOE archer role if you want that. Tbh, you never really need rulers or avengers per se, they are kinda just nice to have. I think what you could do is roll for Arturia, and hope to get Martha too.

Personally, though, I think you should stop if you got Arturia regardless of whether you got Martha or not. If you got Martha, great. If not, maybe try for Jalter (next moth probably) since she's generally just better. You have a better chance of getting Martha, but like I said, Jalter is better, and unlike Martha, she has a x2 bonus against rulers, and while there aren't many ruler bosses, Jalter would be much more useful for them.

Also, after this year, Jalter will only be available in paid banners for a while, and to the best of my knowledge she hasn't had another solo rate-up again in JP, while you could always try for Martha again next year.

I'm assuming you have a high level Hans or friends with supports. That's the only real glaring hole I see. Otherwise yea rolling for Squirtle is great. She's second only to Gil possibly among SSR archers. Martha is a luxury not a necessity. It would be better to save quartz for a good support be it memelin, waver or fluffy tail.