Looking for ascension advise

I'd go with Lily. Since most of the time your support goes out first. Having another waiting in the back is nice. Especially a healer to top everyone off after a big round.
I'm a newer F2P, but I was using a similar strategy with Mash and Iri. I'd have Mash taunt a big wave of damage. Then have Iri come in and NP heal and give guts to the party. Having a dedicated healer is a nice reset to the party halfway through a big fight.

Archer; I have Emiya, and I've used both Arjuna and Atalante as support. I've never had a problem with Emiya's normal card damage. But his NP is pretty sad. It's barely enough to clear a stage farming dailies. Arjuna would be my pick of the 3. Since his NP is the strongest, and he is Arts based. Atalante being quick oriented, and I find her NP gain lacking. Especially since I'm using her as support when farming, and I cant control the CE she has.

Don't know if you've considered this, but in about a month or so we will be getting the prisma causeway event which comes with Chloe Von Einzbern as a wellfare servant. She is at this point one of the best archers (4 or 5 star) in the game, and we will get her at NP5. Imo worth considering using her over Arjuna/Atalante.