On the Subject of Keypads
CJam, 13 12 bytes

qN/(f&amp;{,}$W=


Test it here.

Explanation

q     e# Read all input.
N/    e# Split into lines.
(     e# Pull off the keypad buttons.
f&amp;    e# Take the set intersection of each key line with the keypad, preserving the order
      e# order in the key line.
{,}$  e# Sort the results by length.
W=    e# Pick the last (longest) one.