A vessal is exactly what it suggests. It's a vessal which the spectre connects itself to that acts both as a conduit and an anchor for the spectre to use in the mortal realm. Though it can be literally anything that has some reflection or representation of the spectres nature in it, but it is most commonly human.
The spectre itself has no say in who or what becomes its vessal, and even though the spectre can disconnect itself from its vessal and return to the shadowlands a new connection cannot be made until the vessal is dead (or destroyed if it's an object). Which means that the next time the spectre jorneys into the mortal realm it will connect with the same vessal as it did the last time it was there unless that vessal has somehow ceased to exist.
The only things that cannot be possessed are things, or people, who are already magical in nature. Which means that both artefacts, vampires, mages, demons and werewolves are immune to "possession" from a spectre.
While in its vessal the spectre is bound to the limitations of the vessal. Which means that if it's human, the spectre will be confined to this humans limitations (i.e. this humans attributes, abilities etc.). If confined to an object the spectre will have full use of all its spirit stats, except the physcal, but will be limited in movement and/or speech depending on what kind of object it is connected to.