Windows live mail, free from here Windows Essentials - Download Windows Live Essentials is the best.
Anyone who says otherwise is simply wrong as it is a matter of fact not opinion.
Well, Adam, I must be wrong for using the Modern Mail app for the past 2 years without any problems whatsoever. I used WLM when using Vista and 7 for an estimated 6 years. I find the Modern Mail app to be easier to use, especially that it works in conjunction with the Calendar, People, Photos, and other apps which is using the system's efficiency as a whole. It's also walled-gardened so therefore safer to use. I get popup notices even if the app is closed. Also when not in use it goes into a dormant state using less resources, which is particularly handy on a pad, laptop, or hybrid.
If I remember correctly WLM uses POP rather than IMAP that the Modern Mail app uses, which to me is a much more sophisticated technology giving users more options.
Pros and cons as stated in this article:
Post Office Protocol - Wikipedia, the free encyclopedia

POP is a much simpler protocol, making implementation easier.
Email clients use it for cost savings on server space and maintenance.

POP mail moves the message from the email server onto your local computer, although there is usually an option to leave the messages on the email server as well.
Can someone report on whether this option remains in WLM or other programs? I think it is, but don't remember.

IMAP defaults to leaving the message on the email server, simply downloading a local copy.
If no option of keeping a copy on a server, this is quite important if something happens to a system whereas there's loss of data, unless one backs up their email folder. Then why should we, if there's a copy on the server.

POP treats the mailbox as one store, and has no concept of folders
I think this depends on the version of POP.

An IMAP client performs complex queries, asking the server for headers, or the bodies of specified messages, or to search for messages meeting certain criteria. Messages in the mail repository can be marked with various status flags (e.g. "deleted" or "answered") and they stay in the repository until explicitly removed by the user --which may not be until a later session. In short: IMAP is designed to permit manipulation of remote mailboxes as if they were local. Depending on the IMAP client implementation and the mail architecture desired by the system manager, the user may save messages directly on the client machine, or save them on the server, or be given the choice of doing either.
This means a much better searching system. e.g. By date, a word or number (whether in the header or body), folders, flags, etc. Here's a snip in the advanced search in Outlook.com.

The POP protocol requires the currently connected client to be the only client connected to the mailbox. In contrast, the IMAP protocol specifically allows simultaneous access by multiple clients and provides mechanisms for clients to detect changes made to the mailbox by other, concurrently connected, clients.
This means a company or organizations can have an account where multiple users can access it simultaneously.

When POP retrieves a message, it receives all parts of it, whereas the IMAP4 protocol allows clients to retrieve any of the individual MIME parts separately - for example retrieving the plain text without retrieving attached files.
This means I get to see the body before attachments are downloaded which is another safety feature.

IMAP supports flags on the server to keep track of message state: for example, whether or not the message has been read, replied to, or deleted.
So therefore whatever device I use for that account it shows the current state of any email.
Bottom line is that I'm here to state as a fact and not opinion that the Modern Email app included is indeed better in many ways. Also as with other MS apps, it's just a matter of time it will be pulled from the lineup.
To be fair, here is some more facts about IMAP's pros and cons.
Internet Message Access Protocol - Wikipedia, the free encyclopedia
Edit:
Not saying the Modern app is perfect, but personally I never had a problem with it.
http://www.eightforums.com/general-support/55879-wlm-win-8-1-emptying-all-folders.html