Which assassin to raise

I've been looking into this for myself although don't have Emiya so didn't consider them. I gather (mainly from info on this website) that Fuuma Kotarou is an upgrade on Cursed Arm. The others are equal or downgrades depending what you need and likely aren't worth your embers. King Hassan may be coming out soon and will likely become the best assassin although he has a very different kit and role than the others as he doesn't generate Stars well (but strong buster damage and instant death).

Kotarou has the 2nd best stargen of the entire game, after Jack. He is a little stronger than CA Hassan, but is AOE NP is naturally weak. Also, he imposes a lot of AOe debuffs.

Emia Assassin has a very good stargen, good crits, and the only unit with targettable taunt+free stars. Sadly, he has horrible NP Gain, as a Arts Assassin this is sort of a problem, so give him Arts/NP Gain up CEs to compensate that. Also, use him mostly as star generator in Arts Teams.

Kotarou and CA Hassan are for more quick oriented teams.

Jing Ke and Serenity are inferior options.

The best 4* assassin damage-wise right now would be carmilla. It's actually shiki as she's a free np5 but since she's limited and judging from your question, a newer player so you probably don't have her.

Emiya is getting a np interlude later this year though which turns him into the best 4* assassin DPS as his np2 damage deals around np5 shiki damage so there's that to consider.

Outside of that for low rarity servants, fuuma is a good star generator/support. Not a good damage dealer at all. I personally rate Hassan higher. Although he has slightly lower star generator, he has one of the best survivability skill due to protection of the wind which is a 3 hit Dodge on a 5 turn CD(when maxed) which rivals cu cunlain's protection from arrow.

For 3 stars, jing ke will do the most damage. However, other servants are more flexible. Of course 4 and 5 stars will do better damage so try for king hassan or upcoming eor servant.

Hello! Yes Kiritsugu is quite decent and even more so if you have proper support for him. I am assuming you didn't get Shiki as a welfare Servant perhaps since you just started?

Cursed Arm Hassan has great survivability despite his low stats due to his evade skill and he can solve your critical star problems if you have them. He also has low cost so he is great if you're tight on party cost limits. Just don't expect him to do great damage due to his low stats. However, with Kotarou's release, his star gen role was kinda taken over by the said Servant. Since Kotarou has higher stats and overall better stargen, Cursed Arm has stiff competition.

Given the options you have, I would recommend Kotarou over all the others. But I strongly suggest you prepare for the re-run of the event where you can get Ryougi Shiki. She can easily fill your Assassin shortage once you have her.