Best servant class to focus on first?

I would spread the wealth around a bit. No need to have one character at max if the rest are under leveled. First you can forget about Stheno. She is not a very good servant. I wouldn’t get to her till later.
Carmillla is your best bet at Assassin. Ceasar is a very versatile saber and works well in a lot of teams. David is a good archer who can produce good damage through spamming his NP. Cu Lancer is a definite as he is one of the most survivable servants in the game. Pick whichever you like, though I think proto has a slightly higher attack. NEVER underestimate the importance of Mash. First off she is zero cost which will make her a staple in your party. She has the best defensive kit as well. She can boost the parties defense, provide invincible to one party members and has a taunt. So she can agro ST NP when she has her third skill. Keep her leveled up and her skills as well.