Theres no real essential 'fixes problems in Morrowind' mods cos to be honest, its pretty awesome the way it is, and no glarring issues that need adressing.
I would disagree there. The MPP and MCP patches (linked in my sig) do fix problems that will break quests and ruin savegames. I consider them essential and would recommend them to all new players.
Also, Pluto's http://www.gamesas.com/index.php?/topic/1060141-mod-recommendations-for-new-players/ thread. It has lots of good information on where to start. (oops, as posted by Illius above).
Have fun!
Edit: also, when you do start to add mods, be aware that Steam has changed the file dates of the .bsa archives in "Data Files", and newest game resources are loaded over older (by default). So don't forget to re-date your .bsa archives.