Difficult to answer - EasyPHP, as you probably know, was designed to be development platform for local use on a windows platform, not for production use. Worse still the applications involved are neither designed for or optimised for use on Windows - IIRC Apache for one advices against using Windows for production purposes. None of this, of course, means that it won't actually work for *your* application.
If you want my opinion - I wouldn't dream of running a trial or otherwise on EasyPHP. However, neither would I consider doing it on a Micro$oft platform at all, as it just seems like bother for no obvious benefit. So you can see my prejudices
To answer the second part(s) of your question, most modern Linux distros come with all this stuff built in and should be very easy to use - in many respects easier/better than EasyPHP. What you won't get is the nice integrated configuration interface that EasyPHP has, so you may well find yourself having to spend some time with the documentation and find the configuration files you need (although you probably won't have to change them). It is very unlikely that you would have to download
anything from other sites.
I use and can recommend SuSE's distro. It runs Moodle out of the box. The only (very small) issue I have found is that you must specify an SMTP
server for mail in moodle as SuSE's PHP's sendmail interface seems to be broken.