What to do with the bodies
Great question, most of these monsters will look somewhat human after death, this can be a problem if someone see it. There are a few ways to get rid of the bodies. The way I see it. There are two main ways to get rid of the evidence.
Graves being the first. Simple. Easy. Cheap. Graves work well if you're on a budget and want a neat clean up. However, it is not the most effective way to insure the creature is dead. In the case of vampires this is a great option. Stake them to the ground in their own grave. Now if you're 100% sure it's dead and you want to dig a grave may I suggest you dig a two foot by two foot hole twelve feet deep. Not only is it harder for satellites to pick up the hole, but if anything were to come to life again, it would need to claw its way six feet up rather than just standing up and climbing gout the six foot deep hole. If it is something else may I suggest option two.
This is my method of choice, fire. Burn the body of whatever you killed. Ash is easier to dispose of than the body of a creature. Fire works well because it destroys all traces of life that was in the creature making it harder for it to come back. A great way to make sure nothing too powerful reassembles itself anytime soon is to cut it into a few pieces and burn them in different places. The best part is, light it, come back the next day and then bury the ashes 6 feet down. It will be a much smaller hole to dig and a better way to get rid of the big parts.