So I just started getting into this game, and it's getting better and better the longer I play. I looked it up before, but I don't want to miss anything: What factions can I join in Morrowind? What are the pros and cons, if any? I've heard that you can only join so many, some quests can kill other quests, and some factions only let you join if your characters stats are high enough. Maybe it's not a good idea to join factions until I've found them all and can weigh out my options.

The wiki has more info than can fit into one post with a question like this.
There are 8 Guilds/Factions to join, Three Great Houses (can only pick one) and Three Vampire clans (can only pick one.)

http://www.uesp.net/wiki/Morrowind:Factions

Some of the Guilds and each of the Great Houses is geared towards a type of Class. (Stealth, Combat or Magic)

Some factions won't let you in unless your Skills are high enough, but usually this still allows almost anyone to join. But being in a faction that favours Skills you are poor at can cause a lot of hard work for you.

Thanks! It looks like I have to flip a coin for either Hlaalu and Telvanni. Which vampire clan would you recommend I join?

Just like the three Great Houses, each Clan is geared towards a certain type of Class.
You can look at their favoured Skills to see which is which.

There are a lot of caveats that go with being a Vampire though. You can't go in the sun, cannot have conversation with most people, etc. (there are mods which address these things though)

Ok, last question. After I join a vampire clan, can I become human and still be a part of them? Can I become a vampire again and again or only one time like in Oblivion?

If you do the quest to cure yourself of Vampirism, you can never be a Vampire again.
And all vampires will once again be hostile.

I'd suggest going with whatever vampire clan suits the flavor of your character, but purely technically Aundae is best because one of their quest will net you a very good magic shield that you can't get in any other way. The quest itself can be quite challenging though, you have to kill a vampire hunter in broad daylight in the middle of Ald-ruhn.

On the side of fun instead of stats, the Mage's Guild are hilarious. They have a ton of crazy political descent and conflict. The Telvanni are the same way; each of their councilors are insane, thousand year old eccentrics/lunatics, with no remorse for their enemies. The Tribunal Temple have a long, really boring quest which is required for you to join. The Thief's Guild are also pretty fun.

if you join Morag Tong, you should finish all he writs before joining a great house because you will have to house members.

there is some conflict between the thief and fighter guilds so if you want to be head of both, you will need to plan ahead. http://www.uesp.net/wiki/Morrowind:Quests will help.