If you're going to set a DnD game on Middle Earth, you're pretty much forced to be Elf Lords in order to have access to 90% of the system.
The players also probably want to mostly be Elf Lords, though, so this is less of a problem than it sounds like.
You sold me. I'm assuming the players guide is the first book I should start with? After that what should I get so I can run a campaign?
I'll just add that if AiMe appeals to you, just play the game it's based on: The One Ring.
While I have a deep and abiding love for The One Ring, sometimes you just can't get a group to learn a new system. It's great that the core of 5e is flexible enough to easily adapt it to Middle-earth.
Middle Earth never felt like a setting that needed its own rulebook.
You can make this kind of reductionist argument about anything.Middle Earth never felt like a setting that needed its own rulebook. Disallow certain classes, be very specific in the monsters you select and you can use 5E without problem.
Most of the differences between ME and most 5E campaigns is over the game focus and style.

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.