Team composition

squirtoria/medea/hans: good ap spam with buff stealing, charge stealing, and some attack and crit provided by hans. i feel that would work well. that one i feel is well rounded for general use, but you could sub on chloe over medea for more damage if you feel you can get away with it against whatever content youre fighting. could also sub on mash instead of medea for ridiculous survivability and still have squirtoria nuking things and providing np steal.

cu alter/leonidis/nightingale: im a big fan of leonidas plus berserkers and combined with cus natural defenisve skills i feel it makes cu practically unkillable if he wasnt already, but a lot fo characters can provide. leo comes with the added benefit of a buster buff. nightingale in the same vein provides more damage, debuff removal, and heals which is the only sirvivability tool the other two lack as well as having two buster cards to help chain.

okita/alexander/mash: okita and alexander create a high damage pair with their buff and mash provides the defense. lots of 3 stars and lower could be subbed in. caeser, hans, fuuma, hassaan. more or less in that order of benefit i feel. this team is probably the least surviable of them all. but your main damage dealer in okita has her own dodge so it should be fine as long as she stays alive and the rest buff her.

not that thats all you can do. just some ideas

You have literally all the arts pieces except a support. To standard comp is usually dps+support+support with variations existing. The pattern with the dps and some of the supports you do have strongly tends towards making arts teams. Your best team would probably be using Altria Archer for all non lancer fights along with a Tamamo and preferably a waver. You can use a support Tamamo for now since you don't have her but she will be on rateup soon so I would try to get her when she is if I were you. Waver is ideal as he completes that arts stall charge drain np spam team while, well being waver. Mash is an ok substitute for him though post Camelot being able to buff attack and greatly buff defense as well as provide an invuln.

That is your best team but you do have quite a few SSRs and I do agree that all SSRs are worth levelling. For your other pieces:

Kintoki, Raikou, and cu alter are all amazing berserkers but given that you will have Altria Archer, develop them in this order: Raikou>Calter>Kintoki. The one thing Squirtle lacks is an AOE np for farm which raikou is the absolute best at.
Vlad III is a luxury and should be developed last. While he is an arts dps as well, Squirtle is just straight up better.

Okita is arguably the best current saber out due to her hard hitting self buffed quick np. There aren't a lot of supports to make a good team around her but she works great as an independent unit and will be able to handle the lancer heavy quests

Tama lancer is in the top tier of Lancers with a hard hitting ST np that destroys Male servants (of which there are a lot) and has unique skills that can amplify her boons when used right.

Altera, Jeanne, and Chloe are decent options but you have access to servants that are better at providing what they provide. Note: Jeanne will surpass mash once she gets her strengthening.

Pieces you could use: Lancelot Saber, Tamamo, Gil caster (when he comes out), Fragment of 2030 if you don't have it