Concerning the master of death i'm still unsure where the resurrection stone came from. Was Dumbledore just holding it all this time? So he had the opportunity to take the cloak and become the master of death, but never did. It seems to be implied that the title is worthless anyway, and that aside from creating zombies and being able to kill people and sneak about, like Voldemort pretty much, there is no additional ability obtained by having all three artifacts.
Dumbledore and Grindelwald in their youth were both Deathly Hallows fanboys (in addition to planning world conquest).
After Dumbledore and Grindelwald split up, Grindelwald stole the Elder Wand from Gregorovich the Wandmaker (an Eastern-European Wandmaker in the same trade as the UK's Ollivander), because Gregorovich was foolish enough to boast that his wands were superior because he was using the legendary Elder Wand to make them. And then Dumbledore eventually took the Elder Wand from Grindelwald after beating him in a duel.
James Potter had the Invisibility Cloak, which he had inherited through the longstanding Potter lineage, which had inherited it from the Peverell line (the Peverells being the Three Brothers from the Deathly Hallows story). As a kid in Hogwarts, James used it for pranks and mischief. When James became an adult and joined the Order of the Phoenix to help Dumbledore fight Voldemort 1.0, he showed the Invisibility Cloak to Dumbledore, and Dumbledore practically orgasmed, because Dumbledore could see that it was no ordinary invisibility cloak, it was THE Invisibility Cloak, the original one (all the others are plainly inferior copies, and even then they're very expensive). Dumbledore asked James if he could borrow it, to study it, and James (not knowing it's true value) said "Sure". Then James (minus his cloak) got killed by Voldemort. Dumbledore hung onto the dead James' Invisibility Cloak for several years, until Harry came to Hogwarts, and Dumbledore delivered it anonymously back to Harry.
The Resurrection Stone was engraved with the Peverell Family Crest (aka the symbol of the Deathly Hallows) and set into a ring. Voldemort's poverty-striken Grandfather (on his Mother's Slytherin-descended Wizard side of the family) loved to flaunt it as proof that he was better than everyone, despite his obvious poverty. Voldemort killed his grandfather and stole it. He eventually turned it into his first Horcrux. Voldemort did not know that it was a Deathly Hallows (Voldemort was Muggle-raised like Harry and had no idea what such a thing even was). Dumbledore found it while looking for Voldemort's Horcruxes, and when he saw it was a Deathly Hallows he lost his sense of reason and grabbed it without thinking, which triggered Voldemort's trap, which was a Death Curse of some sort. Snape managed to slow-but-not-stop the curse, which killed/blackened Dumbledore's hand. Which is why Dumbledore enacted a suicide plan with Snape, because Dumbledore was walking dead anyways and his death was imminent. Dumbledore put the Resurrection Stone inside Harry's first Golden Snitch and left it to Harry in his will.
Dumbledore was able to see and touch all three Deathly Hallows, but he never held all three of them at the same time, because he returned the Invisibility Cloak to Harry in Year One, and he found the Resurrection Stone in the break between Years Five and Six.
Dumbledore gave Harry the Invisibility Cloak and the Resurrection Stone, but he had planned to kill the Elder Wand and take it with him to his grave. Dumbledore thought that suicide-by-Snape would result in a masterless Elder Wand, but Dumbledore was wrong, and he did not anticipate that Draco would inherit the Elder Wand by simply disarming Dumbledore, nor that Harry would inherit the Elder Wand by way of the Elder Wand following Draco's Wand after Draco's Wand changed it's allegiance to Harry. Harry becoming the Master of Death was not part of Dumbledore's plan.