I’ve always stood by the advice of 1 ST and 1 AOE that you can reliably use in nearly all content, after that focusing on farming servants specifically (except for Arash, I believe levelling him early helps with the EXP grind to level other servants).
Going by this:
Saber: ST- you have both Okita and Yagyu who fill this niche excellently. AOE- best option I can see is Saber lily, but you said she’s NP2 so her damage is going to suffer, I’d say level Fergus or use Chacha maybe.
Archer: ST- Recommend Euryale, she’s an anti-male nuker. Also Robin for high ST damage. AOE- Emiya is an excellent option.
Lancer: ST- Li and AOE- Nezha. Besides them I recommend you level Cu, he can solo a lot of content due to his excellent survivability .
Rider: ST- you missed Kinbro, but Ryouma’s an excellent ST rider, I have him grailed to 90 and love using him (even over Kintoki). AOE- Ivan’s got you covered.
Caster- You don’t have many good options here, but Siege is a great farmer with good damage thanks to NP5, Edison has some support utility but he’s hard to use. I recommend the Caster GSSR for you, if you hit jackpot and get one of the big 4 support casters then great, besides them, Nero, Illya and Sanzang are all great DPS units. the worst you can do is Caster of Nightless City and she while underwhelming can hold down the fort and has some use for her Insta guts skill in CQ content. ST- level Medea, she has insta NP with great loop potential. AOE- Siege, maybe Nursery down the line if you can build her.
Assassin: ST- I see you missed Shiki who is in my opinion the best SR assassin, but you have Emiya who plays similar to her. AOE- not many options but you can substitute with Okitan, so don’t worry too much.
Zerks: ST- Hijikata has you covered. AOE- Chacha, her damage is a bit lower but she’s an excellent option for farming thanks to her battery skill and and defense down, I actually use her for Ember farming . You have Herc, try to get him to bond 10, he’s easy clear mode with his bond CE.
Extra- Level Okitan, alteregoes are one of the best classes you can have starting out, I know cause I had Kiara. I never needed to level any Cavalary units thanks to that till after Solomon. Trust me you’ll be glad to have her. Also try to max her battery skill.
You lack supports the most in my opinion, and good supports can make life a lot easier. I recommend starting with Hans and Shakespeare. After that Mozart, his star bomb skill can help out with crit teams a lot. He would pair well with Yagyu , Li , Emiya Assassin and Ryouma (Also Nursery if you plan to level her). David is a non-caster option, though he’s more of a hybrid support than pure support.
Teamcomps well here are some:
Mash, Yagyu ,Emiya Assassin can form a crit team of sorts . After you level Mozart try Yagyu/Emiya (Assassin& Archer)/Ryouma /Li+ Mash +Mozart.
Also Euryale+mash+support Waver/support Jeanne is an invincible team with high damage numbers against male enemies if you can play it right. You can replace Euryale with Robin and even Emiya (since he has a 3 arts deck).
Hans + Mash + Li/ Yagyu/Emiya(both of them)/Ryouma.
Hans+Ivan/Okitan/Hijikata/Herc+ support Waver/Merlin+ bacline Mash.
Try a team with Okita(saber)+Hans+Mash+taunters+ support Waver (I’m pretty sure most lancer bosses can be dealt with this).
Anyways I’ve rambled a lot, hope its of some use.