Intel cpus should not be a problem. ME is outdated, yes, but you can run it using VMware (or other virtalization software) if you like; on the other hand, if it's just Office docs you need, you can use OpenOffice on Linux. It's best to use the open formats with it, but it can deal with MS Office file formats as well, not 100% perfectly but very well if you ask me (macros etc. don't work at the moment, you'll have to re-create them).
If you pick up an easy-to-install-and-use distribution (Ubuntu, Fedora, SuSE, ...) you should have no big problems. User rights, directory system and such are perhaps the biggest changes from WinME, but nothing you couldn't handle; I've seen a lot of people who I've installed Ubuntu for that have been first-time-newcomers to Linux and had less problems than with Windows, from the first boot. If your attitude is right, you'll have an easy start
There is also an option to use Wine (or pay for Crossover Office for example, but Wine is free and _should_ be able to run Office) to install and run a native Microsoft Office on your Linux. Though if you're fine with using OpenOffice which is very similar to MS Office, I suggest you go that way.