Budget team for Artoria archer

Iri could honestly work why? Artoria's weakness is if some guy NPs her without hard defense she dies of course and Iri could answer that giving Artoria guts and could provide more healing with her skill that increases healing received increasing her tankiness and survivability. That is to say I am assuming you don't have her in NP 2 since your NP loop could be broken if not and what if you needed a heal? Iri would provide that. When you don't then use her skill as simple as that.
But that aside I think the Emiya assassin/Tamamo/Archuria would work since if you're lucky enough the enemy wouldn't be able to NP anymore due to arts crit spamming and charging their NPs so my bet is on him if you want since he could create stars while being an arts servant. Put scapegoat on Tamamo who used Morph though.

Hans is pretty good support for Artoria if you want a crit team. Iri and Emiya aren't the best because Artoria already has a massive heal skill on a short cooldown and she can generate crit stars on her own. As for the NP crit team, use Hans and Tamamo/Waver.

Kotarou for star gen and Target evade.
David for team evade and charisma.
Mashu.
Georgios for tank.
Mozart for arts buff and stars.

I have Arthoria(archer) to and my team
Arthuria with art,np gain or critical ce depend on situation
Fuma , his evade and star Will help arthuria a lot
Waver,tamamo- no need to explain
Mozart- his first give 48 % art effectivnes,and thirdvkskill give 50 star
How to use Mozart?
Put him on backlane until you need him, change podition with fuma then use his first skill for add art effectivnes and third skill to give star.
Tamamo+ arthuria(formal craft ce) + Mozart Will give you around 40+45+40 %of art effectivnees
You can change fuma with Hans if your enemies ia assasins.this strategy also work with other art offensive servant like shiki,Nero,Li shuen, shuten
For Li shuen i tried it with Tesla in event and can kill him in one turn (around 280k damage) and my np bar full again

Squirtoria+Ryougi/Kiritsugu+friend Waver for sustained NP charging and increased non-NP damage.
Squirtori+Ryougi/Kiritsugu+friend Tamamo for big Arts chains and NP damage buffs with some sustain in Tamo's NP
Squirtoria+Hans+friend Jack for more focus on crit buffing and some sustain in Hans' NP

Why are so many people recommending fuuma? He has no passive star gen skills making him a non-ideal candidate for star gen. He has 3 quick deck as well which is not ideal especially since artoria wants to art chain as much as possible to get her np up.

For arts/buster based teams, passive star gen is the way to go so servants with instinct skills(provides stars on use) like Hassan/emiya assassin or innoncent monster skills(skills which generates stars for x amount of turns after skill is activated) like Hans or CEs like 2030.

The simple reason being you always want to use your dps cards if it's available. The only time you won't would be if you did not draw the cards. In that case, you either perform an arts chain for your supports to have their np ready(Hans/mashu) or having a decent crit star generator do a brave chain (any assassin with good hit counts). The standouts for assassins for this would be Jack because...Jack, emiya assassin due to his instinct/taunt, Hassan due to instinct + proof of arrow like skill for survivability.

So in this case, a more offensive team would be artoria/emiya assassin/support tamamo or artoria/Hans/support tamamo. A more defensive line up would be to replace emiya/hans with mashu.