Whether a human that has been and wants to stay vamped, or starting as a Vampire, the very first skill to get is the Cursed Blood skill. This keeps a player a from being revived against the player's wishes. If starting as one of the Vampire classes choose either the Feeder or Predator. The Feeder class gives a bite attack damage increase (40% accuracy and up tp 4 damage) while the Predator skill allows a Vampire to search for prey with the Sharpened Senses skill. The Predator is probably the best to start with.
Once a player gets the Cursed Blood skill, the next step is to either get the Sharpened Senses (see above) skill or bite skills. Bite skills eventually lead to the Plasma Feeding Skill. Plasma feeding is the only way a Vampire can regain HP, and the amount recovered is the same as the damage you inflict.
The best skill after all of these is the Supernatural Senses skill. This skill allows a Vampire to walk by a building and know how many beings are inside (hiding or not). As of 11/18/07, vampires with this skill can no longer sense the presence of other players inside buildings that take up more than one block, like schools, malls, Fort Howard, Twilight City Stadium and the Davis Waste Treatment Plant. If a player's hunting ground is Fort Howard, then this skill is not critical.
Following these, the next skill to acquire should be Supernatural Strength, not because it increases hand damage (45% claw accuracy and 2-3 damage) but because it allows the purchase of the Inhuman Durability skill. This skill lets a Vampire to ignore 1 hp of damage.
The rest of the skills, such as Lunge (attack while getting up) or Defile (smear blood over spray painted graffiti for 3 XP) are nice but not a priority. Silent Whisper is the only truly worthless skill for Vampires.
Other than the Defile skill, Vampires only gain XP by killing Humans and Zombies. Vampires can either wander Twilight city and rely on their Supernatural Senses to detect prey in buildings, or they can stake out a prey rich environment for constant raids. Currently, only Fort Howard affords such an environment. The humans that inhabit the Fort usually hide, necessitating the Sharpened Senses skill.
General survival Tips
A player should find a walkie talkie and join a group as soon as possible (doesn't matter the order). A player's group members can help find prey and offer protection when AP stalled. To break down barricades, try to find a sledgehammer. You can still use some weapons as a Vampire and they work better on barricades then claws or fangs.
If revived, try to find and wear Kevlar Vest (Police Stations, Fort Howard Training Ground) as it will reduce the damage a player receives in combat. You can ask a group member for a bite or head to True Blood Lane (10,1) in Sobersville and hope a Vampire with the Vampiric Infection skill bites the player to death.
Don't waste your XP on skills you don't want or don't need. Since every time you buy a skill, the next skill you buy increases in price, buying pointless skills could hinder you when switching to another race.
NOTE: Some players frown upon jumping out of buildings to avoid being killed when not online. It is seen by some as a abusing the jump ability that was originally intended to help players interested in playing as a zombie. Excessive jumping can lead to a general dislike by the community (forums, wiki, etc.). You have been warned.