What I do to handle my email is somewhat overly complex to post here but in a nutshell:
1) I have a main email account from my ISP. I forward that to a gmail account where I keep all the emails forwarded from the ISP email (I have it set to delete after forwarding).
2) The gmail account has rules set up to file almost every inbound email into specific folders, and mark the email as read. I also have this account globally set to forward everything before it's moved and marked as read to a SECOND gmail account.
3) This second gmail account is the one where I read my emails and delete them after I have read them.
Now, the first email account (ISP one) never has any emails in it because they are deleted after forwarding. The first gmail account contains all the emails but I do not see them on the phone because they are marked as read. The second email account, as mentioned above is where I read everything.
All three accounts are set up on my phone. HOWEVER, when I reply to any email, I change the From address to my ISP address, so the people I reply to do not know I use gmail at all; as far as they are concerned, I am replying from the same account they sent the email to (the ISP account). Sure, people that can read email headers can figure it out but it's really not an issue.
In summary, 1) I still have the POP3 email account I have had for 10+ years but don't have to keep the emails on the server or download to Outlook client; 2) all my emails are filed, archived and categorized on the first gmail account which can be accessed by folder from my device if I need to; and 3) I immediately delete any email that I don't need to action that come from my second gmail account, and if I do need to reply to any email, I click Reply but change the from address so that it's sent using the ISP email's outgoing SMTP server so that the recipient sees the reply from my ISP email address.
I also have gmail set up so that any outbound emails when I use gmail on the laptop/PC browser will be sent through my ISP's outbound SMTP server (there are articles on the net on how to do this). Every so often, I log into gmail from my laptop/PC and file emails that I don't have rules for, to keep the inbox clean on the first gmail account. Best of all, gmail handles all spam filtering for me. Once set up, it works like a dream for me.