A few things about being a Death Eater that I've noticed a lot of fic writers/RPers don't seem to know:
A Death Eater is defined--by Harry Potter Wiki's terms--as a group that "primarily consisted of Wizards and Witches who were radical Pureblood supremacists, and who practiced the Dark Arts with reckless abandon and without regard or fear of Wizarding Law". It should be noted that Death Eaters carried the Dark Mark.
With that being said, not everyone who was a follower of Voldemort possessed the Dark Mark or was a Death Eater. The Dark Mark was considered a high honor among his followers, and therefore people like the Snatchers didn't possess one.
The Dark Mark is located on the inner left forearm on someone. Not their right arm, not on their bicep--the inner left forearm.
It should also be noted that the Dark Mark was a brand that Voldemort himself placed onto his followers; "Lord Voldemort placed the Dark Mark brand on his followers' inner left forearms both as a sign of their loyalty to him and as a method of summoning them to him when he desired."
Keeping that in mind, if you're going to have your character play a follower of Voldemort, it doesn't make sense to have them waltz into a meeting one day and tell Voldemort that they now have the Dark Mark.
"There is no possible way of getting rid of the Dark Mark." This does not mean that you can have Draco wake up one morning and decide to attempt to burn it off his arm and have his attempt be successful, or choose to have Lucius glamour it until it disappears. The Dark Mark fades when it is inactive, but it is always there.
The Death Eaters, supporting Pureblood supremacist views of the world, would not likely be composed of anyone who is Muggle-born. It's not realistic to have someone like Hermione Granger or Colin Creevey become Death Eaters, because aside from the complications that such a thing causes with their characters, it's unlikely that Voldemort would allow two Muggle-borns to enter his exclusive group of Death Eaters.