Firefox is userfriendly enough that you could make the IE icon on your desktop point to it and your family wouldn't notice. In fact, many people do just that.
For the less deceitful user - it works just like IE. It's a box with back, next, reload, stop and an address bar. You can get the Googlebar extension installed which is identical to the PC one except for pagerank. Bookmarks are handled exactly the same way except you can have seperators and it's called 'Bookmarks Toolbar Folder' instead of 'Links'.
And of course there's the security, pop-up blocking, adblocking, tabbed browsing, mouse gestures... but they are either optional extensions or transparent to the former IE user.
As far as I know, when installing Firefox you choose either 'All users' or 'Just for me' and can set the default browser as Firefox for you alone. If you can't, it's more likely a problem with XP because the developers would have added it.
Mozilla is an open-source project that transformed the old Netscape 4 source code into a much better browser. However, mail, chat and other features got incorporated, plus tons of misc. options. It became bloated. It's still incredibly useful for web developers but it takes too long to load and too much memory for some users.
So Phoenix came out - a cut-down version of Mozilla, for Windows, which dispensed with most of the unneccessary fluff and made it leaner, smaller and faster. It has no mail client, chat or address book- just the browser. Then the name had to be changed for legal reasons to Firebird. However, there was an SQL server project called Firebird - although it wasn't a legal requirement, in good faith they changed their name once again to Firefox. So all three names are the same project. It's been Firefox since 0.8 and will probably continue to be in the foreseeable future.
As for a mail client, well, Gmail requires no mail client
But for POP3/IMAP, Thunderbird is a good project. It's identical to Firefox in that it takes the mail part of Mozilla and cuts it down to run faster and on its own.
Get it here.