So, what's wrong with webmail? There's no inherent advantage to having the messages downloaded to your machine if you have internet access, and most webmail interfaces now have settings to allow some set amount of messages, usually driven by date, to be downloaded to the machine for offline access.
I would never, ever, use POP unless it's the only protocol a given e-mail service provider has, and there are very, very few for whom that's the case these days. You should not be concerned about exactly where your e-mail client stores anything, as that's what it does behind the scenes, and any attempt to play with its message databases is bound to end in tears.
The Windows 10 Mail App is not a full-featured e-mail client. If you're used to Outlook (as in the program that's part of Office), Thunderbird, Opera Mail, or another e-mail client elsewhere you'd be far better off to download and install it on your current machine. You would also be well-advised to set each and every machine that's accessing the same e-mail account(s) to use IMAP access to get to them so that you don't end up with the insanity that generally comes from using POP access on multiple machines and having missing messages on all of them depending on when the other(s) downloaded messages. IMAP dispenses with all that mess, and when it became obvious that most people wanted to be able to access the same accounts from multiple devices that's one of the reasons IMAP came into being.
Brian AKA Bri the Tech Guy (website in my user profile) - Windows 10 Home, 64-Bit, Version 1803, Build 17134
Memory is a crazy woman that hoards rags and throws away food.
~ Austin O'Malley