Which of these methods of hashing passwords will be most secure and most hard to find hash collisions?
Neither of these should be used for password hashing they have been proven to be insecure:
MD5 from Wikipedia:
The security of the MD5 has been severely compromised, with its weaknesses having been exploited in the field, most infamously by the Flame malware in 2012. The CMU Software Engineering Institute considers MD5 essentially "cryptographically broken and unsuitable for further use".
SHA1 from Wikipedia:
SHA-1 is no longer considered secure against well-funded opponents. In 2005, cryptanalysts found attacks on SHA-1 suggesting that the algorithm might not be secure enough for ongoing use,[3] and since 2010 many organizations have recommended its replacement by SHA-2 or SHA-3.[4][5][6] Microsoft,[7] Google[8] and Mozilla[9][10][11] have all announced that their respective browsers will stop accepting SHA-1 SSL certificates by 2017.
Much more secure hashing algorithms exist such as SHA-2 or 3 which should be considered.