The Moto Z, on its own, is very thin at just under 6 mm. If you're not planning on opting for any Mods, then you'll want a case with great protection against drops, since a spider-webbed screen is abstract art that's pretty hard to appreciate.
One of my favorite cases for any phone is Spigen's Rugged Armor. It's a one-piece TPU shell that's sturdy and strong, but flexible, with excellent shock absorption, helping to prevent cracks should you drop your Moto Z.
The TPU's texture provides excellent grip, and the cutouts for the camera and ports are precise, giving you a really well-fitting case. The volume and power buttons are covered but very responsive.
Speck's CandyShell cases feel very solid in the hand, and the Grip series adds ribs in all the right places, so you can firmly hold onto your Moto Z at all times. The outer shell is a hard yet flexible polycarbonate, while the inside is soft and flexible "Impactium" (Speck speak).
The two combine for excellent drop protection (aided by the reinforced corners), and aid in preventing scratches and chips, especially thanks to the raised front bezel, which protects your phone when laid face-down. It's available in clear or a range of colorful options, so you can fit one that matches your personal style.
If you don't buy it for the name alone, grab the Unicorn Beetle PRO because it's one of the best rugged cases around. If your job requires you to be physical or you're just rough on your phones in general, then you'd be hard-pressed to find a better case that's this protective without being overly bulky (expect some bulk, but not a ton).
This case comes with a belt clip that's attached to a front cover, so when your Moto Z is on your hip, its screen isn't getting mangled from rubbing up against you and your clothes. The Beetle has reinforced corners to provide extra shock absorption, and the built-in screen protector will help to keep your Moto Z scratch-free.
The Incipio case for the Moto Z is made of two layers to protect your ultra-thin phone from ultra-hard surfaces. It's not the sleekest case in the world, made up of a two-layer system comprised of a silicone liner and "rigid plextonium shell," which helps against impact.
One of the best things about the case is that it's the perfect thickness to keep the protruding camera ring protected without adding considerable thickness to the 6.1mm phone.
It's available in five colors: red, black, gold, silver, and pink.