Need Help regarding units

Jack is the best star gen in the game so fits in a quick team as well as a buster crit team.
Vlad is good in whatever arts spam team you make but if you want good units with an art spam team you need a Tamamo caster if not your own at least a friend's. Mozart works too as support in an arts team. Other good units in an arts team would be Orion but failing getting her, Euryale will do.

Cu alter works in a buster crit team but really Karna is amazing in a buster crit team.

Of your remaining pieces kintoki Rider is good in a quick team. The rest are mostly just good for farm or just good pieces in general that need teams built around them rather than fitting teams. Jeanne is a support that can fit all three teams as her role is primarily defensive. In an arts team though, she definitely would improve survivability of the entire team being able to NP often. Having Martha helps too to remove jeannes NP debuff in any team.

Arts spam- You have vlad who is a good np spammer in a proper team. I don't know how good he would be since you need waver and tamamo to help boost his below average np gain. I would go for personally Mozart/Vlad/(Support)Waver/ possibly for less damage instead of mozart go for jeanne.

Zombie team- This one is a lot easier simply since you already have Jeanne for team comps I personally would go for (support) tamamo for her heal and cooldown reductions then Jeanne since she will never die and can protect from np's and then hans again for his heal and defense up. Tamamo/Jeanne/Hans backline can be people such as cu alter and mash who can both survive and increase defense.

Quick team- You already have jack which basically means you don't really need to make a quick team to have stars since she can cover the whole team, so if I would make a team where crits are the goal and you want to quick basically every turn. Jack/kintoki rider/ and support is really up to you waver is good but you might be better off using maybe scathach or okita who can deal consistent damage.

Crit Buster- I actually don't have much experience in this, but I do use a team that can be classified as this which is Jack/Jeanne(alter)/support waver you can just switch or jeanne for cu alter, but since you don't have a good attacker to use the crits with I would go instead Jack/Support attack with crit absorption and damage so people like Jeanne alter/ than a leaved Hans for his critical up. Don't worry too much of np gen in this team except for hans, because in a good buster crit team the crits will usually do more damage than the np.