If you're just getting started in Product Management, don't join a startup.
Why?
Startups (in the early stages) are incredibly volatile places to work. Goals change every 5 minutes, people come and go, crazy targets get set. Often the focus is on pace over quality and mastery (why spend 6 months building something infinitely scaleable only to learn that nobody likes what you've built). The Founders personalities tend to dominate the culture.
Don't get me wrong, for all the reasons above they can be extremely rewarding and lucrative places to work. Prove yourself and you'll get the chance to progress quickly, work on really interesting things, and take on responsibilities that you wouldn't get close to for 10 years at a large stable organisation.
BUT
For obvious reasons they have little time for mentorship and skills development. They need people to join and start contributing right away.
It can be incredibly difficult to orientate yourself in the chaos of an early stage startup. You need some experience before you have the confidence to spot situations and appropriate responses, and be able to hold your own against generally very passionate and dominant senior leaders.
A better choice is to join a mid sized company (200+ people) with a small but growing product team. There, you can learn alongside others, gain experience and get a feel for areas that interest you. They will probably have the resources (and time) to offer training and support.
Find a company that has a good product culture, where there are still some interesting problems to figure out (as opposed to a massive company where the focus is really on optimisation and not breaking anything).
Finally, a great tip when thinking about your career is to always think a couple of jobs ahead. Where do you want to be in a few years, and therefor what experience and skills do you need to accumulate in order to get there.