Generate a password

05AB1E, 19 17 16 bytes

Saved 1 byte thanks to Kevin Cruijssen

áΣl}.γl}éεgyθJ}J

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Explanation

á                  # keep only letters in input
 Σl}               # sort by lower-case
    .γl}           # group by lower-case
        é          # sort by length (stable)
         ε    }    # map each to
          g        # its length
             J     # joined with
           yθ      # the last letter
               J   # join to string

C# (Visual C# Interactive Compiler), 105 bytes

x=>x.Where(char.IsLetter).GroupBy(a=>a%32).OrderBy(a=>(a.Count(),a.Key)).Select(a=>a.Count()+""+a.Last())

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Thanks to dana for bringing it down to 105 bytes from 138 bytes.

Japt v2.0a0 -P, 14 bytes

f\l üv ñÊ®ÌiZÊ

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f\l üv ñÊ®ÌiZÊ     :Implicit input of string
                   > e.g., "Kitkat Tango"

f                  :Split to an array of characters
 \l                :  Matching RegEx /[a-z]/gi
                   > ["K","i","t","k","a","t","T","a","n","g","o"]

    ü              :Sort & group (Preserves original order within each group)
     v             :  By lowercase
                   > [["a","a"],["g"],["i"],["K","k"],["n"],["o"],["t","t","T"]]

       ñ           :Sort
        Ê          :  By length
                   > [["g"],["i"],["n"],["o"],["a","a"],["K","k"],["t","t","T"]]

         ®         :Map each Z
          Ì        :  Last element of Z
                   >   ["g","i","n","o","a","k","T"]
           i       :  Prepend
            ZÊ     :    Length of Z
                   >   ["1g","1i","1n","1o","2a","2k","3T"]

                   :Implicitly join & output
                   > "1g1i1n1o2a2k3T"