I understand that as of the last hard fork, the minimum mixin has been changed from 0 to 2. However, is this an effective baseline? Or is there a higher selection that users can or should choose that would ideally guarantee a private transaction?
There can be no such thing, because "private" is not well defined. Even if you were to ring sign against every single other output on the chain, everybody doesn't use Monero, right ? Moreover, there is a difference beteen untraceability and unlinkability, and more (tracking first relaying node, etc). Different facets with different solutions.
Generally, the higher the mixin, the larger the anonimity set. However, when you start getting into the less used mixins, such as 73 or 352, two transactions using mixin 73 will be likely to be sent by the same wallet. This may be an argument for quantizing mixin values.
As an aside, the wallet default mixin is 4, which provides more privacy than the bare minimum allowed by the network.
It is probable that minimum mixin will be increased in one of the next few forks, since this was one of the recommendations of https://lab.getmonero.org/pubs/MRL-0004.pdf.