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.