How do I become a Vampire right after exiting the Sewers? Eating the heart or Contracting it?

Help me Choose the best yet Right Race, Birthsign(I was thinking of Serpent) and Major Skills.

Is it fun being a Vampire?

http://uesp.net/wiki/Oblivion:Vampirism#Becoming_a_Vampire

Find a nearby Vampire lair. Memorial Cave just southeast of the Imperial City, due east of the Arcane University across the water is one that is fairly close. Fight a vampire and survive the fight. You will very probably catch Porphyric Hemophilia during the fight. If not, fight another one until you do.

Wait 3 days and sleep. You're a vampire.

Some people like playing a vampire. I don't. I think it's one of those "try it and see" things.

As far as "build" goes, I can think of a few ideas...

For race, Dunmer is good, because their fire resistance will cancel out a lot of the vampire's fire weakness. Altmer vampires are extremely vulnerable to fire, so that's probably not the best racial choice. The vampire's Night Eye power would be pretty useless to a Khajiit.

The only birthsigns I'd stay away from are the Lord (weakness to fire) and the Apprentice (weakness to magic.) The Shadow would be pretty useless (but it is anyway.)

Or you could really roll with it and go Altmer with the Lord as a birthsign. Fire would be your kryptonite.