lammert - 6:44 pm on May 26, 2010 (gmt 0)
Basic HTML should just work fine on both Windows and Linux hosting. The main problem you may face is that Windows is a case-insensitive operating system while Linux is case-sensitive. This may cause some file reference problems or missing URLs if you didn't carefully use one case type for your references.
WordPress itself doesn't let you touch the Linux level. The whole administration of your site is done with an intuitive web-interface control panel. Only the installation will need a few commands to put the files on your hosting account, unpack them and get the WordPress installation running.