I would've gotten to work on this earlier, but I had some outside business to attend to. I decided to put the One-Star and Two-Star Servants together on one document. This is also a test to see how well this format works before I use it with the other ones. This list is done in class order. I've compiled this list based on personal experience and various comments around the Wiki. Of course, feel free to suggest edits in the comments.
Arash[]
Two good CEs would be Purely Bloom and Heaven's Feel. Of course, Arash's main gimmick is his NP, STELLAAA!! If you want to use it multiple times, throw Bath of the Lunar Goddess on him and equip Anniversary Blonde. Of course, if you just need to use his NP once, Kaleidoscope will work just fine. (Or Imaginary Number Magecraft, if you're like me and don't have Kaleidoscope) Another good suggestion is Demonic Bodhisattva if you want to just load up his NP and fire. If you want him to deal damage then fire off his NP at low HP, use a CE that has NP gain or damage increase and Guts to make sure it is used. (Ex. 2 Gods 3 Legs or Chaldea Lifesavers)
Musashibou Benkei[]
Based on his NP and skills, I'd say anything that would increase NP gain would be good enough for him. In addition, anything that increases debuff success rate or just increase his defense in general. He'll do well when paired up with Tamamo and a damage dealer as a debuffer. His bond CE and Record Holder can help him fill this role.
Leonidas[]
THIS IS SPARTA!!! A good idea for him seems to be Divine Banquet so he can get more NP when he's attacked and in turn use his NP more quickly. He does best in an Arts Team with Buster NPs. If you're impatient, equip the always-reliable Kaleidoscope. (Or Imaginary Number Magecraft if you're me)
Saint George[]
Any Siegfried Master's best friend. His best CE is probably his Bond CE. If you're going to mostly pair him with Siegfried instead of using him as a tank, Kaleidoscope will be good so he can get a "Dragon" trait on an enemy so Siegfried can take them out more easily. Divine Banquet can also do the job as well.
Edward Teach[]
NORMIES EXPLODE!!! He's best on a team of all-females as a support. For ultimate usefulness, use his bond CE on a Buster-based team. In addition, the CE Gentle Affection will also be useful for him.
Hans Christian Andersen[]
I've seen multiple suggestions for him. Two of the most recommended I've seen are Demonic Bodhisattva (Because Noble Phantasm) and Fragments of 2030 (Because CRITS FOR EVERYONE!!).
William Shakespeare[]
He's a budget Buster-team support. One of his skills increases critical star generation, so I guess Fragments of 2030? His best CE depends on what's on your team. If you're using a lot of Berserkers, Outrage or Grand New Year will help. If you're not using zerkers or your team is generally not a glass cannon, use Ox-Demon King or Walking in the Spring Breeze.
Wolfgang Amadeus Mozart[]
Hm...Fox's Night Dream, Divine Banquet, Prisma Cosmos, or Fragments of 2030 depending on what your team comp is.
Sasaki Kojirō[]
The Savior of France. It's REGEND, he doesn't need any CEs. But, if you really need any, give him something that boosts Quick Card effectiveness or Critical damage.
Cursed Arm Hassan[]
Personally, I would use something that would increase Quick Card effectiveness or help generate critical stars.
Charles-Henri Sanson[]
I use CEs that increase Quick Card effectiveness or NP gain to try and get the Instant Death off faster. He's more difficult to use because of how picky his skills are. If you're using him to fight a large number of enemies with the "Human" trait, he'll really shine through. He'll benefit from CEs such as Walking in the Spring Breeze, Glass Full Sweet Time, and Covering Fire in that case.
The Phantom of the Opera[]
Anything that increases Quick effectiveness. Something that can boost Critical Star Generation. (Ex. Be Elegant)
Mata Hari[]
To boost her Charm success rate, Elixir of Love. Anything with NP Gain to get her NP faster.
Spartacus[]
The man that is pure muscle. Best CEs for him are probably Mikotto! Bride Training and March of the Saints. Of course, because he's a berserker, anything that helps increase Buster Card performance would be helpful as well (ex. Verdant Sound of Destruction).
Asterios[]
Kaleidoscope, Imaginary Number Magecraft, Prisma Cosmos, etc.
Caligula[]
Just use his bond CE or Limited / Zero Over. Anything Buster-boosting will do great on him, since he's mainly a damage dealer. However, Maid in Halloween also seems to do well on him.
Eric Bloodaxe[]
Use something that increases Buster Card effectiveness. Or try slapping Golden Millenium Tree on him and pair him with a healer.
Paul Bunyan[]
For wave clearing, use Kaleidoscope and the like.
Angra Mainyu[]
AKA Angry Manjew. He's a no-star, but I decided to put him on this list anyway. He's not a tank and he hits like a wet paper bag, but he does best as a Debuffer it seems. His NP does its best when you have Guts on him. Overall, he seems like one of the more difficult servants to use. I'd say to go with his Bond CE or something with Guts, but I've seen people suggest Knight's Pride and a crit-booster servant. I've also heard of someone using Golden Millenium Tree on him.