How to choose the right VPN for my iPhone?

The vast majority of content you’re likely to access when on a public WiFi network is almost certainly end to end encrypted to begin with, so using a VPN adds nothing when it comes to security or privacy. Quite the opposite as has already been stated.

As for your second use case, I have to assume it’s either an employers network or a schools network.

In that case, the answer is simple… stay off that network if you’re going to be accessing things that could get you into trouble.

The only valid reason to install a VPN on your phone is because your employer or school requires it.

Otherwise, ignore the hype about a VPN improving your security. It won't.

What it will do is slow down your phone and put money in the pockets of the companies selling this stuff.

Simply because they are not protecting your privacy/security and in many cases are doing the exact opposite. Your IP address is already hidden behind a router so there is no access to your device. With Public Wifi, you would never want to access any banking or financial website whether you intend on using a VPN or not. Just a few of the reported problems are available here with the most common Nord VPN being fined multiple times for violating their users privacy. Simply search the forums here using the Search option on the top of this page. You have all the information to make an informed decision. Good luck with whatever you decide.

https://www.pcmag.com/news/7-vpn-services-found-recording-user-logs-despite-no-log-pledge

https://www.foxnews.com/tech/massive-free-vpn-data-breach-exposes-360-million-records

https://www.malwarebytes.com/blog/news/2021/03/21-million-free-vpn-users-data-exposed

https://cybernews.com/security/25-million-free-vpn-user-records-exposed/

https://gist.github.com/joepie91/5a9909939e6ce7d09e29

https://overengineer.dev/blog/2019/04/08/very-precarious-narrative/

Said as simply as possible. NO, don't install a VPN. They are NOT needed and cause more issues than they could possibly solve. Plus, they offer a false sense of security, which is quite the opposite.