One size fits most on the aprons. They're wildly too big for my 5'4" size 4 body, and they even fit our 6'5 built-like-a-linebacker partner with minimal issues, so I suspect you'll be fine.

Hats you'll likely have to purchase from the coffee gear website if they aren't required by health code in your area. Google Starbucks coffee gear and you'll find it.

I’m 275 and 5’. I think you’ll be okay.

I'm 5'5 and over 300 and it fits fine with lots of string to spare in the back. you'll be fine!

You’ll be fine with the apron. I’m 5’3 and plus size, the apron fits me fine. The hat will be provided by your manager if the state requires you to have one. You can always go to Walmart and get a plain black hat if you’re concerned about it.

I’m 5’5 and wear around a 18/20. The apron itself goes almost to my knees and I have a lot of excess tie in the back, enough that I can double back and tie in front too! My only complaint is the sizing on the top portion is a little weird. If you have larger breasts I definitely recommend loosening the neck strap, just be aware the top will shift around a bit and might look a little weird.
As for the hat, if you are not required on by your state and your manager doesn’t give you one, then I wouldn’t worry too much about it. If you want something I definitely recommend getting a black visor from Walmart. I was provided a hat when I began my training, but the hat isn’t my favorite as it gets my hair really greasy after a shift. Visors are my personal favorite for hat options, and if you or your manger doesn’t care about the logo, I recommend getting a plain black one from Walmart or n the cheap and decorating it with pins (it’s what I did with mine). If you need a logo hat, Coffee Gear has them but they are a little too much for my taste.

I’m just a little taller than you and a size 16/18 and they fit me just fine!