What the Heck is That?!?

I haven't found any solid rules in 5e D&D for adjudicating Nature and Arcana checks to learn more about monsters. My players (who for whatever reason haven't all run out and purchased a copy of the MM and memorized its contents; I suspect "not being a teenager" to be high on the list of reasons ;) ) ask for these rolls a lot. I certainly don't mind; part of playing under the philosophy that "it's not the DM's job to balance the encounters; it's the players' job to unbalance the encounters in their favor" is giving the players enough information to make intelligent decisions about which encounters they want to tackle and how.

So that means, whenever they encounter an unusual critter, they'll ask what they know about it and I'll ask for either a Nature or Arcana check. Which do I ask for? Arcana for the following creature types:

• Aberrations
• Celestials
• Constructs
• Elementals
• Fey
• Fiends
• Monstrosities
• Undead

All the rest us Nature checks; I'll take the highest of either Nature or Arcana for dragons.

So the players roll their dice (usually they all do this) and I start with the second-highest roll ("Ok, the bard knows blah-blah-blah...") and then move to the highest ("... and the wizard can also tell you blah-blah-blah.")

So what do I tell them?

On a roll up to 9:
I tell them they don't know much. I tell them maybe what the thing eats, and a rumor (that I openly label as such) that might be true and says more about the setting than the monster ("The shepherds down by Greenford have trouble with these things coming out of the forest and swiping sheep every three or so years.") and may or may not be true.

(In general, whenever the players make a knowledge check, I tell them something no matter how badly they roll, even if it's not immediately useful.)

10-14:
Either an immunity or resistance, or one major attack or defense the creature has. If it has a defining characteristic (like a displacer beast's illusionary positioning) they'll get that instead.

15-20:
All immunities, resistances, and vulnerabilities, plus one major attack or defense, and any not-obvious forms of locomotion. If they ask, I might tell them about senses, but not give ranges, as well as relative speeds (faster/slower than you).

21-25:
All-of-the-above, plus highest and lowest stats, all senses and their ranges, plus their speeds.

25+:
Pretty much anything they want to know. If they roll above 30, I'm just handing them the book to peruse.