It really doesn't matter with regard to e-mail messages themselves (as opposed to attachments).
Whether you use POP or IMAP you are downloading the message bodies to your computer (and that's in webmail, too, otherwise you couldn't see them). Depending on how you have things configured in an e-mail client you may or may not download attachments in advance as some can be set to download them only if you select them.
In the end, it really doesn't matter in this day and age if your e-mail provider is doing virus/malware scanning, and many do, and you're using some sort of antivirus/antimalware combination that scans all e-mail messages during download, and that's how most are set up these days.
If something makes it through from an untrusted source then I, like Louis, decline to click on any link or attachment in the message and just delete it.
The vast majority of my access to e-mail is via webmail or a mobile client.
From a non-security perspective, I always recommend that folks who have the option use IMAP access, which keeps all their messages on the server with local copies of the message bodies created in the client for some period of time, which eventually get deleted but will be retrieved again if you want to read them at some distant future time. Data centers have backup and restore protocols that are a lot more rigorous than most home users ever will and, in addition, IMAP automatically causes all devices that access the same e-mail account(s) to remain in sync with each other.
Edited by britechguy, 25 March 2018 - 10:12 AM.
Added bit about IMAP at the end
Brian AKA Bri the Tech Guy (website in my user profile) - Windows 10 Home, 64-Bit, Version 1803, Build 17134
. . . the presumption of innocence, while essential in the legal realm, does not mean the elimination of common sense outside it. The willing suspension of disbelief has its limits, or should.
~ Ruth Marcus, November 10, 2017, in Washington Post article, Bannon is right: It’s no coincidence The Post broke the Moore story