Koutarou or Emiya (Assassin)

I would recommend Emiya his deck is better for it and his targeted taunt + someone with evade can make up for Artoria's lack of a hard protection skill. The downside is a bit less stars but I'd say its more than made up for with taunt and the ability to decrease enemy NP gauge even more often.

Kotarou or hans are your best F2P Choices. Hans offers buffs and substantial healing with crit chance up and consistent stars. If you managed to farm His rightful place CE from the fate zero event it would be ideal. Kotarou offers an extra evade and much higher star gen in exchange for giving no buffs.

TLDR
These two are the best budget options with hans taking priority. Hans offers more damage and consistency overall while Kotarou offers more survivability and stargen

If it's a question of Emiya vs Fuuma. I'd say Emiya. Tho he provides less stars than Fuuma, he makes up for it with more Arts chains for Artoria, and both of their NPs can decrease NP gauge as well making for a decent stall. You can give him star gen CEs to make up for his star gen. I personally prefer The Classic Three Great Heroes on him as it provides Star gen+, NP damage+ and starting CE all of which Emiya really needs.
Yes, Fuuma does have a targetable evade, but if you play your cards right, you'll barely even see enemies threaten you with strong attacks and Mystic codes can also help.

Outside of your question, I think Hans can better fill the role of star generator for Artoria. A good level'd 3rd skill can provide Artoria with decent stars and his triple A deck can help with Arts chains. Han' NP can also buff star gen drop and with Artoria's good hit counts, I think she may be able to provide stars for herself in some situations.

Would recommend emiya simply because he has an instinct skill. Instinct skills are basically skills which generate stars on use like emiya's Taunt.

Reason being you want your main dps, which in this case artoria to attack, as much as possible. Using cards to generate stars is by far one of the least effecient way to do it unless the servant's name is Jack. In scenarios where artoria is not in the card economy, emiya is decent with a 4/2/6/8 hit count deck which means a qbq/qaq chain generates about 30ish stars.

Pairing them with mashu is great as she has a targetable invul along with damage cut/def which is stackable with artoria's own arts buff+def buff. All of them share 9 arts card as well inclusive of np cards which means generally easy art chains.

Hans is decent as he has innocent monster which produces a solid 9 stars every 3 turns out of 5. Same reasoning with emiya as he doesn't eat into your card economy and he has a great np as well.

If you have caster Liz, she's one of the best welfare servants for crit star generation as she has BOTH instinct and innocent monster like skills. The Innocent monster skill provides a solid 12 star for 3 turns every 5 turns while her instinct provides 8 every 7. She also comes with triple arts deck.

Lastly the best crit star generator imo would be Lancelot saber. He too has both instinct and innocent monster like skills but at crazy values - 15 stars every for 3 turns every 6 and 20 stars every 6 turns. This coupled with his decent 3/2/4/5 hit deck means a respectable amount of crit stars generated. He is also arts focused and can arts chain.