When to use my Quartz

Depends. Do you aim to roll for the strongest characters or the ones you like?

I think the Alter Egos from the Fate Extra event are fairly good for newer players, since they have broad class coverage.

Raikou is making her return in a few months. She's great at farming in most cases, and even though she's AoE, she's still fairly good in single-target scenarios, especially since you have Merlin to support her.

During Summer, we'll get last year's rerun first, which includes Archer Artoria, who's all around an amazing servant.
Then, the new summer event, which brings Caster Nero, arguably the best offensive caster in the game.

That's short to mid-term.

If things go your way or you're willing to save for longer, the last couple months of the year include some nice returns like First Hassan and Musashi, as well as amazing new additions like Ereshkigal and Hokusai.

Again, it largely depends on what's your criteria for rolling, so if you can provide more information on your tastes, we can grant better advice.

I don't know how complete is your team, but I wouldn't recommend a new player to hoard...unless you want to go through the frustration of playing for a long time with crappy 3*.
If you want to go ahead and do it anyway, the notable servants this year are:
Raikou --Onigashima (Rerun)
Artoria Archer --- Summer (Rerun)
Gilgamesh -- Fate/Extra CCC Pre Event Pick up
Merlin --- 10 Million Campaign
Hokusai -- New Year Campaign

For the 4* department 2 very good servants will also be added to the game:
Summer Raikou (Lancer)
Munenori Yagyu (Saber)

Most things in this game come down to rolling for the servant you personally like, whether they're good for gameplay or not. The ideal upcoming servants for this year, in my opinion, are:

1. Ereshkigal
2. King Hassan
3. Metlilith
4. Sherlock Holmes
5. Abigail Williams
6. Raikou (Berserker)
7. Munenori Yagyu
8. Nero (Caster)
9. Gilgamesh
10. Artoria (Archer)

Each one of these is a solid servant among the best in their niche. None of them will disappoint you. (And yes, I know Hokousai arrives not too long after Abigail, but still technically doesn't come out in 2019).

Also of note: BB, Kintoki (Rider), and Nobunaga are welfares who are getting releases/reruns this year who are very solid servants. Try to pick them up.

Here's my strategy, as "mostly" F2P (only spend for GSSRs):

My target is to roll for support servants (who are mostly casters): Merlin, Waver, Tamamo, and eventually Skadi, plus maybe CasGil and Helena. I will throw a few tickets (1-5 or so) at servants who seem to good for gameplay purposes (e.g., Archer Gil comes to mind).

The rationale is that I am just never going to get a lot of 5* servants (or even 4* for that matter) from the gacha with just my free SQ and tickets. I don't know if anyone's exactly figured it out, but I'm guessing I got maybe 150-200 rolls in my first year, and will probably get maybe 100-150 or so in the second (since a lot of the SQ is from story, and I've finished up through Solomon).

Thus, I need to get the most bang for the buck here. FYI, I'm not at all interested in waifu/husbando servants. They are all just chess pieces to me, so that is also a consideration. By having my own support servants, it gives me the flexibilty to go to my friends list for damage-dealer servants, of which there are many that fit better in one circumstance or another. I'd also be able to pull off things like double-Merlin/Waver/Skadi.

Luckily, I got Merlin last Xmas, and Waver with the GSSR, so I'm pretty happy at where my teams are. Will probably try really hard to get Tamamo on her next solo rank-up, then Skadi next year.