The way I play vampires (i.e. what powers/weaknesses they have, their appearance and how they reproduce etc.) will depend on the vampire lore I have based the world/my vampire character on, as well as that sim's personality and story. So the possibilities are practically endless! For example, in my main save vampires rule the world from behind the scenes - they're in the media, the police, the government, everywhere and anywhere you can think of! "The greatest trick the Devil ever pulled was convincing the world he didn't exist", right? They stop ageing both physically and mentally once they become vampires (I play with ageing off and age up sims manually). They can eat food for pleasure or appearances (although they don't need it) and don't need to feed on other sims, but are cursed with a terrible, unending thirst for plasma, which over time leads them to lose all trace of their humanity with Dampened Emotions and an Insatiable Thirst. Their dark form simply consists of completely black eyes and the classic two vampire fangs, and this only appears when they're fighting or feeding. They have evolved to be able to walk in sunlight (Sun Resistance), but are still sensitive to it (Day Phobia). They don't sleep in coffins or turn into bats or anything like that, but they do have Vampiric Strength which increases with age, as well as the Vampire Creation ability. Only the eldest surviving vampire, their leader, has the ability to Command other vampires, as their vampire blood all traces back to him. He's one of the original vampires or the offspring of an original vampire and completely inhuman.
My main vampire sim was originally born in the 15th century and suffered an extremely traumatic life before becoming a vampire as a young adult. He became one of the most powerful and feared Grand Masters, second only to the eldest/leader of the vampires himself, but unlike the others never truly lost his humanity and instead chose to become a Good Vampire and Tamed his Thirst, so he now tries to live like a human. Sadly there is no cure for vampirism in his world which is part of the tragedy for the immortal vampire, and due to his dark past he suffers from Eternal Sadness and Fitful Sleep. He also has a slight Undead Aura about him because he's so old and because he's a Guilty Drinker so he often becomes anxious/stressed around normal sims, which can sometimes make him seem odd and uptight to strangers. As for children, he has an adopted daughter with his (werewolf) partner, but while rare it is possible for male vampires to have biological children with human female sims. In my head I like to think this child would be a 'dhampir' or half-vampire - basically human but with improved health, longer lifespan and sensitivity to the supernatural. I have another Grand Master vampire in a different save with a human girlfriend and plan on him turning her once she has their daughter (and later turning his daughter in a planned ceremony once she is of age and has had a child and so on - thus the family tree can continue). He also has plans for vampires to enslave/take over the sims world with him as the new leader and an army/club of vampire offspring that will follow his every command. >:)
Vampires are very versatile in TS4 as well as fiction. There are so many different takes on vampires to get inspiration from and no 'wrong' way to play a vampire in my opinion. Just let your imagination run wild and have fun! :)