According to this Microsoft page
, Office 2003 is compatible with Windows 7. So if you must use this version (I guess you must if your mom says so, right?) then you should be OK.
I tend to use web-based email these days, so I can't say much about Windows Mail (Live or otherwise), but previously I was using Thunderbird. I also saw other people using Outlook ad other clients, I did not see a lot of difference, they say Outlook is not secure though.
That said and having voted for 7 x64, I would recommend installing Windows 7 32-bit on your laptop, even if you are putting in 4 GB of memory. I am using 64-bit myself, but to be honest, compared to my dad's 32-bit version, there is not much difference or advantages, especially for mundane tasks - text editing, internet and email, and so on. I guess your mom is not a gamer, right? She probably does not run memory intensive calculations as well. Video editing? Maybe, but then you would need a more powerful machine. For general users, I think 32-bit is still simpler to use, there are less compatibility issues, and less possible confusion.