"... What was a thing that was either really useful to you personally when you were a new parent OR a thing you wish you'd had. ..."

Baby sitting services that will care for newborns are tough to find, but anything you can do to give respite to the young mother (and probably, the grandparents) for a few hours, will, I'm sure, be more greatly appreciated than you can ever know. I and my ex-wife were 19 and living independently when our first son was born, and the bone-tired fatigue that boy created in both of us in the first weeks, I still remember, more than 35 years later. I think we each would have sold a kidney for someone to have taken the boy, for one night, while we got some sleep.

She might appreciate a new outfit that is NOT maternity wear after the baby is born (here a gift card to, say, Old Navy would be the ticket.) My daughter who is normally really into clothes was not thrilled with her lack of something cute to wear after the Grandbun made his arrival-this being because of course she was not yet fitting into her prepregnancy stuff. (She is NOW but that's almost ten months later.)

As a 16 year old, I would have loved new clothes. I'm sure she would appreciate a gift card to her favorite shop or department store, or even a couple of carefully chosen comfortable outfits. Trendy T-shirts and cute yoga pants that she can lounge in. I didn't want to wear anything with a button or zipper for weeks after delivery. I didn't necessarily want to head out to the salon right away either. Some yummy smelling bath products might be a better idea.

My mother had me when she was 17. She probably would have loved decent pots and pans or new towels and sheets, or more likely, family support and visitors. Is she living with her parents or in her own place?

This sounds incredibly corny but the best gift you can give your niece is to tell her: "You're going to be wonderful mother." Tell her this out loud. Write it in her card.

Offer babysitting time. Even if it just means taking care of the baby while she is taking a nap, taking a bath or just going for a walk.

For the reasons paulsc said.

Offer personal support as LoriFLA suggested.

Parenting lessons. Seriously. i think everyone should take them, but people know who have come from very dysfunctional backgrounds that have taken many do an amazing job. And it is a job.
That reminds me i have yo call someone.
A bunch of monopoly cards with your number on the back tied with a nice bow, for emergencies such as needing to take a shower or freaking out, asking ridiculous questions.
It's good to have someone you can call with ridiculous questions.
Hell, i want someone i can call with ridiculous questions i have answered as soon as i've asked them.
A freaking tiara and an ipod, preprogrammed with a range of everything.
Hell, i want a tiara and an ipod.
i'm having a tiara and ipod moment right now.

I was hardly a young parent with my first, and even less so with my second (mental note: get his foot unstuck from between the crib bars when he eventually realizes it's caught), but holy cow, having a lifeline is terrific. The first birth was tremendously rough (anything with the acronym NICU in it is bound to be), and among the things lavished on us that stood out: an offer to come do laundry (accepted), homemade food that could be frozen and microwaved/baked, babysitting time so we could have a date.

One that was over the top was a personalized baby quilt hand made by the mother of a friend's life partner. I don't know her and what she knows of me is either second or third hand, but she was moved and it moved us back.

1. 6 mo. of diaper service. . .

2. Nicki (velcro) diaper covers. . .

3. One of those ear thermometers. . .

4. A jogging stroller, or a quality stroller with good wheels. Can be used.

I was 18 when I had my daughter and my favorite gift came from an old friend who sent me a ring. It wasn't that the ring itself was so great, it was that there were so many presents for the baby and that was the only thing that was just for me. It made me cry - when you're young like that and you've just gone through this intense, exhausting, insanely physical experience it's kind of hard to have all attention focused on the baby and none on you. I mean, I was all focused on the baby too, don't get me wrong, but a gift that was completely not baby related was the most wonderful, unexpected thing and I've never forgotten it.