Who to keep and who to trash?

Mashu, hans, leondias, arash, ca hassan

Based on the servants I can see:
Level Hans as he's one of the best supports till you get an SSR caster support like waver or tamamo.
Mashu: because she costs 0 and gets several buffs including being made into an SR servants post Camelot. Also best kouhai.
Kiyo: To provide a decent damage dealer.

Gonna need a full picture to give any more info

Leonardo and Francis will be your best farmers. Ibaraki is your best boss killer. William and Hans plus a tank to go well with Ibaraki. Mash is great because she can give Ibaraki invincibility and 20% NP. Leonidas is also good because he also has a buster buff. Get David to at least 2nd ascension for the aoe evade skill.

My personal set up would be Ibaraki, Hans or a tank, with a support waver. In the back I'd have William (switch him in when you're ready to use Ibarakis NP anf buster cards), David if I know my enemy has an aoe NP, back up tank if they dont, and in the last slot I would have Cu because he's a cockroach

You can keep:
Saber: Ceasar, his skills are good and his NP is great as well for a 3s. Gilles is meh.
Archer: You can keep all of them specially Arash since you can use him for farming purposes.
Lancer: Keep Cu (Proto), he's good since he's an offensive version of Cu.
Caster: Da Vinci, for obvious reasons (5s) and great for farming, Medea for Bosses, Hans (Survivability) , Mozart (Arts) and Shakespeare (Buster) for Support.
Assassin: Fuma for Star Generation because of his AoE quick NP and quick cards though his damage is not so good. You can use Cursed Arm Hassan as an Alt but Fuma is better if you wanted more consistent Damage. We will get Shishou in the coming weeks, she's 4s for free at NP5 so you can use her.
Rider: Drake for farming but you can also use Ushi for Boss Battles.
Berserker: I personally keep Kiyohime (NP 5) for waifu reasons but she's a good farmer, just slap Kaleidoscope then use the Mage's Association Mystic Code to instantly use her NP. Tamamo Cat is also great. Her NP generation is good but the stun on her NP is not. Ibaraki for Boss Battles or single targets.

Seeing your full list:

Ibaraki, Tamamo, Hans, and mash would be good targets to develop initially in that order. Leonardo can be levelled instead Tamamo cat and does provide support in addition to damage but I think will take longer to max ascend.

Of what's left over (all of these could be levelled after the first 5 I've mentioned above): Medea is amazing as a boss buff clearer which requires minimal investment, Medusa is a solid 3 star rider for farm but Ushiwakamaru is better overall on bosses due to her ST NP. If you want a budget Saber, the only one better than Ugly Basta-i mean Caesar is Bedivere who you only get after Camelot anyway. For archers it may be tempting to get Emiya up first but he has a very meh and unbalanced kit until he's fully developed which takes really really long. Robin hood would be a good option to get up early as with minimal investment he has an ST np that smacks. But ultimately I'd recommend David as he has an ability that is a godsend against most AOE Boss NPs. For assassin, Fuma generates the most critical stars so Fuma.

First I would save everyone. You never know what special bonus one might get during an event. Even lvl1 they can be but in the back row for farming bonus.
Of the servants on your list ones that are always on my teams are Ceasar, David, Emiya, Ushi, Cu, Hans, and Fuma.

Best from each class:

Saber: Caesar - Decent ST saber with team support potential.

Archer: They are ALL good. Robin is a nuke (massive NP damage, not much else); David is very good support - has a party-wide dodge; Arash is a farmer - Strong AOE NP; Emiya is mediocre now but will eventually be a very good crit servant.

Lancer: Leonidas - Tank; Cu - Better survivability + damage. I'd go for Cu first since Leo is a bit more niche and harder to use properly.

Caster: Hans - Best Crit support in the game; Medea - Spammable NP with debuff; Da Vinci - a farmer, but she's a five star so that makes her worth levelling; Mozart - strong crit/arts support. No real priority here, they're all pretty great, just depends on what you need, though personally I would leave Mozart for last out of all of these.

Assassin: Fuma - best star generator in the game (aside from Jack the ripper).

Rider: Ushiwakamaru - has very good skills that can support her team; Francis - One of the best farmers in the game. I would prioritise her. Also put her in your support slot for lots of friend points.

Berserker: Ibaraki is your best, prioritise her. Tamamo cat is also a good farmer, so don't neglect her either, also, same with Francis, put her in your support slot = friend points.