I think two important characteristics are

• The importance of the theorem itself
• The extent of connections within the subject

These two are not, of course, mutually exclusive!

This book is a recent discussion of mathematical style which has 99 proofs. A really great read.

@BOOK{Ording2019,
  title =     {99 Variations on a Proof},
  author =    {Ording, P.},
  publisher = {Princeton University Press},
  address =   {Princeton and Oxford},
  year =      {2019},
  isbn =      {9780691158839},
}

and this book collects together proofs of $\sqrt{2}$ is irrational.

@BOOK{Duchene2010,
  author =       {Duch\^{e}ne, L. and LeBlanc, A.},
  title =        {Rationnel mon Q: 65 exercices de styles},
  publisher =    {Hermann},
  year =         {2010},
}