https is the security that encrypts your data between the device & the site. Ideally your bank uses certificates with good ciphers & extended validation so that anyone on the public wifi cannot attack your traffic. Others on the same network can see you are sending data to the bank's site but they cannot see what that data is.
https://www.ssllabs.com/ssltestcan tell you how good the bank is dong their job with the certificate & it's security. Be sure to check the site that you login to some banks have many site addresses with different certificates & security levels.
Provided you do not blindly accept dialogs similar to 'this certificate is bad, do you want to ignore' you should be safe on public wifi as the certificate system can't be altered in transit (at least for good, modern security).
Proxies will not add extra security.
A VPN can add extra security when using a public wifi network, that wraps all traffic up inside encryption - very similar to https sites but it also handles http sites and other traffic. Be sure to use a VPN you trust if you choose to use one. They will help with open wifi & other public access points.
Cellular data is not immune to being attacked or manipulated by bad actors within cellular companies so you should consider using VPN's there too if you are paranoid about privacy/ hacking etc.
TOR is just a 'chinese whispers like system' that passes data from place to place in an attempt to hide the source. Each node cannot read the content, only the exit nodes can see the data. It wraps the data in layers of encryption and each node peels or adds one layer (like an onion, hence 'The Onion Router'). It's actually an elegant system invented by the US navy. You probably don't want to use it for banking as you will exit in some random country, your bank may see that as suspicious & can potentially lock the account - VPN's can have the same issue but most paid services allow you choose from a few exit locations.