Help With Team Building?

Idk if you've considered it, but you could replace Vlad with any arts DPS in that team comp and it'd work. Eg, saberlot if you want an arts-crit comp to deal with lancers (he synergises well with Hans), Orion if you want to deal with males/sabers (if you are worried about Camelot, definitely level her. She makes it MUCH easier).

Idk what sort of team comps would work for Karna since I don't have him, but he is definitely worth levelling if only because he is the best AOE lancer.

First off find someone with a levelled Tamamo so you can use it as friend support.

You're right. You have three arts dps in Vlad, Lancelot and Orion and potentially a third in Emiya but I would suggest not levelling him. A Tamamo would just complete the set and you could run whoever your dps is with Tamamo and Hans.

Your main dps other than against archers or where you have class advantage should probably be Lancelot since he is an arts crit monster that does good damage and can generate his own stars. With a Hans in the party also generating 8 stars a turn and his own 20 from his fully levelled third talent, you'd have enough to guarantee crits about 70% of the turns roughly and thus to use his np often.

As for your other servants, Orion is a very decent Archer but the niche she shines in is anti male fights where using her second skill in an NP brave chain you can nuke down a male servant with some huge burst. (Personally I prefer Euryale though for that roll due to her multitude of stuns and np control skill). Vlad is very fragile as a berserker so bring a taunter while he sets up. Hans and tamamo should be able to heal back some of the damage he takes but he is very vulnerable to a stray crit killing him although his guts skill helps there a little. Jeanne is a very niche pick. Her np is quite nice for enemy servants with AOE nps (like Titoria) as are her resistances but the stun is annoying. Best kouhai actually reasonably is able to approximate what she can bring to the group at a cost of zero. Oh and Karna is a solid buster crit lancer for fights where you won't use dadcelot.

More on the subject of best kouhai. Failing getting a support friend with a Tamamo, or even if you get one level Mash as the zero cost is amazing and lets you pick 4 expensive servants with expensive CEs versus having to mix in lower quality ones. Not to mention Mash becomes a complete monster of a defensive servant post Camelot. For perspective, Jeannes np gives invulnerability which is great at the cost of a self stun. Mash is able to give a 50% mitigation in addition to a 2500 damage cut as well as a 30% attack up to all servants other than her post Camelot. And her np is easy to charge too by using her third skill which is a taunt and using her arts card as the third card. She is truly a tier 1 R and then SR all for the cost of 0.

I agree with the above. Arts is your best team. Mash Hans and waver are universal supports. Shakespeare and later Merlin can be the support to any buster damage dealer.
However, you can also build a quick crit team.
1. Karna will be your main dealer.
2. Leonidas can taunt buster up and build stars, all of which Karna wants.
3. Kotarou can build stars and has utility with dodge for Karna. Alternatively, CA Hassan also builds stars and is more survivable.
4. Caesar can be your hybrid dealer/support with 3 buffs for Karna and a strong NP of his own. However, you are most likely facing archers with Karna so might want to just have Hassan instead.
5. Cu fsn will be your backline last man.
Alexander and ushi are not recommended despite team buffs due to stealing stars.
For team tips it is important to know synergy. Servants should increase each others strengths and cover up weaknesses. This is why supports are crucial. This is also why quick is harder to use due to the lack of a dedicated quick support.