Can I make a coupon that only works on a first order or for certain customers?

Yes. Go to Marketing → Coupons and click + New coupon.

• Tick First order only for a welcome-style code.
• Set Customer eligibility to Only these customers (or All except these) and enter their emails, one per line.
• Use Product eligibility to limit the code to certain products or categories.
• Add a Per-customer limit, Total usage limit and Valid from / Valid until dates if you need them.

The Analytics tab then shows the redemptions and total discount given for each code.