Choose Argon2i or Argon2id for secure password hashing on a website?
It depends. If you use weak parameters, then no matter what algorithm you choose the brute-forcing can be done relatively easy.
Think against what risks do you want to protect passwords. Argon2d gives some possibility of side-channel attacks. This is relatively complex and expensive approach. I'd suggest you to estimate the risk that somebody will pay a lot of money to implement side-channel attack. If you are implementing an application where passwords protect banking transactions of millions of USD, then the risk may be higher. If you are implementing an application focused on cooking receipts or traveling recommendations, then may be nobody will be willing to pay a lot of money for a side-channel attack. Then Argon2d may be a perfect choice for you.
I would suggest following (it is a matter of taste): Take Argon2id, it combines advantages and disadvantages of both Argon2d and Argon2i. It combines advantages of both. Pay better more attention to the proper selection of tuning parameters.