First, werewolves are perhaps the most fleshed out in the group next to ghosts, as we are given the impression that werewolves for the most part may not like going wild and attacking people, with few exceptions like Fenir Greyback. And while there are other werewolves that were on the side of Death Eaters, it was an interesting note that they joined Voldemort for the promise of a better life. Furthermore, we know that unlike other series... lycanthropy seems to not be hereditary, though I can understand the concerns that individuals would have, as children could be harmed by a werewolf parent that is unable to control their violence (and another reason for his caution with Tonks).
Next, we come to ghosts, whom are said to be those witches and wizards that did not wish to pass beyond the veil either due to fear of death or some other thing. Given Harry's timeline, with the story happening in the 1990s for the most part, this opens an interesting question being "why are there so few ghosts?" It is an odd question, yes, but in theory there should be more ghosts. Which leads to the next question, what makes a person eligible other than the three requirements of magic, regret and fear? I would like to say that forcible death would be one of the major requirements (Nick got his head cut off, the Grey Lady got stabbed, and the Bloody Baron committed suicide). However, this leads a major opening to another ghostly character in Professor Binns, who more likely than not just died in his sleep. So it could be that those with more forceful and sudden deaths are those more likely to choose ghost hood than those that do not, making Binns exceptional instead of common. This would also connect rather well with how people do tend to assume that the places where individuals are murdered may be "haunted."
Moving to the next (yet less fleshed out) are the inferni. Inferni being things of limited intelligence that do simply what they are commanded to do, and not much else. This goes close to the traditional notion of a zombie, as the servant of a necromancer in voodoo. However, it's made rather clear that there is no spell to revive the dead, but only to reanimate them, leaving some question as to the use of infernis as anything aside from a shock tactic by dark wizards, as other things can be animated, such as statues, and these would be in theory, much, much harder to destroy, as well as easier to come by if the statues were hit by a gemino charm. So what makes inferni special? Really, I'd have to wager that human bodies "take" to the magic a little better. As we can infer, charms on objects tend to fade after a while and most magic (save dark magic) can be undone. So from that, I will assume that inferni MUST be killed by a dark wizard first, and then "re-animated" by that same dark wizard.
Lastly, we have what we have the least information about, with vampires. Now these are strangely the most unacknowledged aspect of Harry's world. They are mentioned, from time to time, to describe a person based off of how they act and look, meaning that they should look human, but we see a slightly different idea based on the outline on Pottermore as part of the sorting quiz. We even see a vampire briefly at Slughorn's party, but the beings themselves have no real description. From that, we will be once again going into head cannon territory, and assuming the following:
- Like in popular fiction, vampires are "undead" beings that were bitten by another vampire
- Vampires can have offspring with the living
- Vampires distain garlic
- Vampires suck blood
- Like werewolves, the majority of Vampires were once wizards or witches.
- Vampires generally seclude themselves from muggles, witches and wizards as per the statute of secrecy
- The ministry provides support for vampires through donations of blood
This is all extrapolating from the sources, and keeping in mind that as per Fantastic Beasts and Where to Find Them, vampires are beings, rather than creatures, and seem to be able to control any bloodlust they have based off of their presence and assumed protection by the ministry. In truth, it makes some sense for vampires to be classified as beings, and "domesticating" themselves, though it still raises question as to them being half of the reason merpeople and centaurs opted out of being classified as beings (the other part being hags). It follows that vampires are most likely not entirely "domesticated" and do hunt and harm people, giving some reason for centaurs and merpeople to opt out due to that.