First
No version of Windows 7 comes with an integral e-mail client, though some PC builders preload Windows Live Mail, or Windows Live Mail 2010.
Next
Neither Outlook Express or Windows Mail can be installed on Windows 7. The last version of Windows compatible with OE is XP. Windows Mail was an OE replacement for use on Vista only.
Third
Windows Live Mail can be used with ANY e-mail service. You are not forced to use it with a Hotmail account. It can be used as a simple POP/IMAP/SMTP system, with normal offline access. The Gotcha is that by default Live Mail 2010 tries to create a Windows Live account using the e-mail address as its credentials. This is an under-the-counter attempt by Microsoft to enroll you in the Live service and so get you using their cloud services. Examples of this are that by default if you try to send an attached image by e-mail, Live 2010 instead uploads the image to their servers (in your Live space account) and then sends a link. Theres a workround but its fiddly. Also you can get round it by setting the flag which tells Live 2010 not to "log in" on startup (all this does is stop it logging into a Live account - its does not stop e-mail)
The key thing to remember here is that a Windows Live account can use ANY e-mail address - it does not have to be a Hotmail/Live e-mail address
The original version of Windows Live Mail does not log you in in this way - the downside is that its less intuitive and Microsoft don't support it any more on Windows 7. The upgrade to 2010 is supposedly mandatory through Windows Update.
As for Outlook, if you want that you will have to purchase Microosft Office.
Alternatives?
Thunderbird
https://www.mozilla.org/en-US/thunderbird/
The Bat! (you have to pay for it)
RITLabs.
Zimbra desktop
Email, Calendar, Collaboration | Find Zimbra Products (free for the client software -intended as an Outlook replacement)
Claws
Claws Mail for Windows (open source Linux program ported to windows - supposed to work well, I've never had any joy with it)
PS - before anyone suggests it, there have been a number of attempts at porting the succesful Ximian Evolution Linux program to windows I've never managed to get these working stabily. I just went looking to get the latest versions and I see the company which had them on its website has closed its download page - I think its worth giving that one a miss.
PPS - just thought I'd take another look at Zimbra as its been a while since I used it. Wow. Its come on a lot since VMware took it over from Yahoo. Looks a bit strange - the look is more Unix than Windows, but it seems really slick in the way it works.