BCrypt works fine, but I wouldn't say it is "2016-era security practices". It was written in 1999 and hasn't had as much scrutiny as SHA or Blowfish (although it is based on Blowfish).

Regardless, using a salted, multi-pass algorithm will keep everything nicely secured using nearly any hashing algorithm.

Remember the goal is not to crack one user's password using a brute force lookup table, it is to crack everyone's password.