Where do I go from here?

You have some of the best Support Servants in the game, Waver, Tamamo and Nightingale, so I would say focus on the characters you love, that should always be a priority, as well as covering the servant classes you don't have Single Target NP Servants for. For example, i don't see Archers in your line up above, so I would suggest saving for an Archer you like. The next chapter of the story has 2 ST NP Archers joining the roster, one is an Arts one who would benefit for your Tamamo Arts buff, or you could save and wait for Artoria Archer in the summer banner revisit. Also don't see any Lancers, so keep an eye out for a lot of them in the summer banner revisit. Since you have great Arts support, I personally recommend focusing on Arts Servants, or if you like Buster Servants, go for them and remember that Merlin returns later in the year. Ultimately focus on characters you like and can have fun using.

Raise Lord El Melloi for general utility since all team comps here can use him.
Raise Tamamo and Lancelot for good Arts support/damage dealer.
Raise Medb and Heracles/Kintoki for a good Buster team (Medb can raise their ATK by 40%).
Then raise Nightingale and Nitocris because they're cute and good supports.
Your servants allow some great combinations, but be careful since they're very expensive to max (52 of each type of gem to max out skils)

Lord El-Melloi II is a priority, max him, max all his skills (in order, 3->2->1), he's the best farming support, and can make anyone extremely powerful and dureble. Fits in any team.

Tamamo-no-Mae is the second priority, her skills at max level have just 5 turn cooldown, she's perfect for arts team, specially stall, has unique cooldown reducing in her NP+ AOE charge in it. Can make Arts NPs offensives a nuke, just use her with arts teams, mind you, and you're set.

Your Kintoki is the rider or the berserker?

Gameplay wise, raise Lord El Melloi II A.K.A Waver first. Like mentioned before, he fits into any team.

Cheat engine/Waver > all of your unit except for waifu/husbandos.

After Waver, strong and tough Zerker like Herc can carry you almost everywhere.
Well that's for easy mode everything, don't use double Waver or Waver + Merlin or Waver + Tamamo if you want some challenges.

If you can't beat harder content, use this : Hercules or any Buster servants + Waver + Merlin.

Honorable mentions :

- don't forget to cover each class department.

- make CE bombs, you're gonna find it's really useful for long term Investment.

- don't always relies on Waver, Merlin or Hercules. Hone your skills by using non-broken servants or even low rarity unit.
Good master/pilot skills + good servants = GGWP.

- practice using solo servant like Chu/Nero/Chu Alter or other anchors, in case something goes wrong you can clear ''leftover'' enemies that have wiped out your party members.
For example, the team comps : Rider Georgios lvl 1 + Lancer Leonidas + friend Herc lvl 80 Bond CEs ( Castle of Snow CE ).

- prioritize to use class advantage system first and if you're fighting multiple classes, Berserker is your best friend.

What does "new" mean to you? Cause I've been playing for about a year and your line-up shames mine.