Lancelot (Saber), Mash, and Tamamo-no-mae Effectiveness

It depend on the situasion, for some hard fight like Nero fest your composition is good enough and you don't want your damage dealer get random critted and get screwed up.
Options for Crit star generation and Crit strength best goes with double Hans with the cost little bit of your sustainability. Though my suggestion is not really recommended, you can try it of.
Double Hans with 2030 or other Crit CE generation equipped can produce a min of 20 stars for every single turn with only 2 turn CD. Also never underestimate his Crit strength buff.
Almost all F2P player can use this composition, considering he is free unit and cost efficient on any team and also have great capability.

my personnal opinion:
give lancelot(saber) star gathering ce
give mash/or whoaver you want fragment 2030
give tamano: more healing stuff though i prefer hans (bcs i have no tamano)
or any other star makers

I think Waver or Hans are more better than Kouhai. If is interesting to have Mashu and Dadlot in team, but for gameplay issue
Waver/Hans+Tamamo works better.
Because
(1) Mashu has 2 Art cards, so does Saberlot. So is even harder for RNG Art chain.
(2) Saber and Mashu have very close star adsorption, it is somehow a hidden issue for Lancelot waiting for his 2nd skill cool-down.
(3) It is even better to have critical-up skill from supports to obtain more damage. And Waver/Hans can also provide attack-up buff further increased Saberlot's attack.
(4) Mashu has amazing defense-buff for the Dad. Yeah. But Hans also has good defense + healing for Saberlot, and Waver as good defense and debuff to enemy. Meanwhile, Saberlot's drawback can be recovered by Tamamo's 3rd skill+NP healing.
(5) It is also good to have Hans and Waver for Tamamo because of Waver's NP charge and Hans's 3rd skill (off course Saberlot will use his 2nd skill, but sometimes RNG make him out of card but quite abundant of stars in specific round, or rounds in his 2nd skill's cooldown) to charge Tamamo's NP faster.
(6) It is a decent idea to have Kouhai with Saberlot. But I think if you have Tamamo as core as Art team then Waver and Hans are better. If you wont put Tamamo in then Kouhai is more suitable like Saberlot+Waver/Hans+Kouhai.
(7) For JP challenge quests, yes a combination of tanky+damage is a better choice. But in NA, Lancelot's critical could kill almost all bosses in few seconds. So it is better for more damage at least now.
(8) Generally not an bad idea for an better critstar generation. But 2030, and some servants can provide star using skills (yeah, Hans) rather than weak Quick card (it is already Art-oriented team). And almost all servants with decent star generation (cards, not skills) in NA are not compatible with Tamamo.

In most circumstances, the ideal team composition is Saber Lancelot + Tamamo-no-Mae + Waver (preferably with Fragments of 2030). If you don't have Waver, I think Hans is a better frontline support choice than Mash, since he's an all-around great crit support unit. His skills give you stars and crit damage, so you can either use them to plug the gap when Lancelot's skills are on cooldown or overlap Hans's crit damage up with Lancelot's for big burst potential. Plus, his NP can give you attack up, defense up, crit gen up (don't underestimate this - because Lancelot has high hit counts on Quick and Buster and crits so often, he can actually generate some stars from cards alone), and healing to supplement what you get from Tamamo.

Some servant you might be considered and for me this is some good Crit Gen and Strength servant yet :
- Waver ( no explanation required ). This man is a monster.

- Jannu, she can draw decent amount of Crit star you needeed, of course must be equipped with good Crit CE gen. Bonus durability for ya : ) Weakness ! Pretty similiar problem with your composition.

- Mozart, if you don't have any Tamamo or Waver he is a decent alternative. 1 turn guaranteed Crit for your carry, also pack with Def down and Art steroid. Weakness! Glasscanon art team detected.

- Caesar, has atk up, Crit strength and NP strength. Can work as Damager semi support for your team. Weakness! Can steal Lancelot stars and you gonna see Faber level Crit damage.

- Helena, decent battery, star gen, Def down and powerful 3 cards buffs. Weakness! Freakingly long CD in opposite with her powerful kit.

- Marie Caster, good for Lancelot star gen and she also has star gen, atk up and Crit STR up. Weakness! Sustainability sacrificed for more power.