Archer

Wouldn't they compete for the crit Stars? Besides it's rare to need both a saber and an archer in the same Quest. But i'd say Atalanta if you really want this combo since her NP Will get you a shitload of stars for 1 turn (Though simply using Jack is better for star gen) or Nobu if you also bring Jack and want to get some high damage crits.

Kogil has charisma and the highest attack between 3* Archers If i'm not mistaken, the problem is his NP is AoE and is more a debuff than DPS. For crits i'd still prefer Nobu because she has a crit dmg boost and is 4*, so higher stats and a Special attack skill

If you are asking for an archer to generate stars, I do not recall any of them exactly excelling at that except for maybe Atalante's Noble Phantasm and Chloe when we receive her in a few weeks. For the most part you will be better off using Assassins such as Jack or Fuma.

Archers innately have a higher Star Gather than Sabers as well so yes their is the chance they will collect the stars over him unless he is under the effects of his first skill.

If you are looking for archers who can also serve as crit damage dealers then Nobunaga, Gilgamesh, Billy the Kid, and Emiya all have skills that are suitable for that role. However Emiya will suffer until he gains his Hawkeye Skill Upgrade in the coming months.