There are ten different Factions/Guilds you can join right away.
None of them are "better" to join than the other. It is just based on your skills.
You can see them detailed http://www.uesp.net/wiki/Morrowind:Quests.
Each character can only join one Great House, but you can join as many Guilds as you want. Although a few have some conflicts that will force you to choose one, like the Fighters vs Thieves, or the Mages vs Telvanni.
Check what the Favored Skills and Favored Attributes are for each Faction/Guild. Join the ones that suit you best, otherwise you will have a very difficult time gaining Rank. Most people join one Great House and one or two Factions, it depends on how you want to roleplay.
Some general tips:
- Make sure you start with a weapon skill as a Major of at least 40, and use weapons of that type.
- Keep your Fatigue full as often as possible. Being tired will make you fail at almost everything.
- Pay attention if you get Diseases or Drained skills. These can be cured with potions, spells, scrolls, or most conveniently at Temple/Imperial shrines (most towns have one.)
- When doing quests, read what people say carefully because they usually give you much needed hints/directions. Your journal will not always remind you of these.
If you have played Oblivion or Skyrim before, there are many differences to be aware of. This is very handy to read: http://www.uesp.net/wiki/Differences_Between_Morrowind,_Oblivion,_and_Skyrim
All the links for info and tutorials on how to find/use/install/manage mods can be found here: http://www.gamesas.com/topic/1305729-mod-recommendations-for-new-players/
Also has all the links to tools and patches you'll need.
And other peoples mod suggestion lists
etc