What is the best way to organize access to privileged functions in smart contracts?

There is no signular best solution, each has strengths as well as drawbacks. The most simple option is using an ownable contract but it is also the least secure option. A combination of access solutions significantly lessens the impact if an account with privileged roles is compromised or acts maliciously.

A DAO (decentralized autonomous organization) is a system of contracts that allows control of processes through voting, providing a decentralized way to control smart contracts. The voting is held on-chain with tokens.

Is it a good idea to implement a custom solution for access control that tailors all your needs?

Usually no. It’s better to use already audited and audited solutions unless it’s inevitable. This will minimize the risk of introducing bugs to crucial parts of smart contracts. If you need a custom solution, be sure to test it and make an audit from a trustworthy company.