Who to focus on raising

Cheapest? Probably Fran. None of her mats are particularly difficult to get, unlike the others who need claws, hearts, and tearstones.

However, of them, the best is probably Cu Alter.

Do CuAlter first, with his survivability and being Berserker, that will save you a lot of trouble. He holds out pretty much on his own once you level him up.
Vlad, due to his low NP rate, is pretty much tied up with Waver and Tamamo, and need higher levels of skills.
Fran is great for farming and Ibaraki has some survivability as well, but not as much as CuAlter or Heracles. She is still useful for high difficulty quest though.

For gameplay reasons def Cu Alter. For waifu reasons, Fran or Banana Republic Oni. Fran may be the easier one to level based on mat collection but as someone who has her and levelled her before herc, my level 50 herc was outperforming her at level 70. So I just max ascended her and have left her alone since only occasionally using her as an opener with kaleidoscope to cast her np and then swap her with someone else

If you don't have an arts comp and need solo target DPS:
Cu > Ibaraki > Vlad > Fran

If you have arts heavy comps:
Vlad > Cu > Fran/Ibaraki

If you finished all singularities and need to farm faster:
Fran > Cu > Vlad/Ibaraki

Generally speaking, 4⋆ servants require less ascension materials but skill-up material seems similar across the board.