What size would be appropriate for me? I'm 173 cm or 5 feet 8.11 inches tall. The frame sizes I'm getting are 16 inch or 17.5 inch
Don't be confused by bike size - the 16-17 inch measurement is a measurement of the bike frame - from the center of the bottom bracket to the top of the seat tube. If your choice is mountain bike, that size sounds close. At your height, according to the charts I saw, you're probably closer to 17-18 than 16-17.
There are a bunch of bike sizing tables on the Net. Personally, I've always preferred a slightly larger bike when given that kind of choice, but it's really a matter of personal comfort.