Cryptographic algorithms compromised and alternatives?
Should you pick AES, Twofish, AES(Twofish) or Twofish(AES)?


You should pick AES.


  Also if you should choose Twofish, is it post-quantum computer
  algorithm proof?


There's no current publicly known attack that breaks Twofish any faster than Grover's algorithm (using quantum computers), so it is as secure as AES in that regard. However it is likely much more difficult to securely implement Twofish than it is to securely implement AES (due to the large secret S-Boxes) and the last meaningful cryptanalysis result against Twofish is more than one and a half decades old because research focused on AES.