There is, unfortunately, neither a best way, nor a standard way. I have lived through several mergers of companies, who then spend inordinate grief combining incompatible parts databases.
Different people, and different companies, feel they need different information.
There is a different between what information is retained by purchasing, which should be everything, what is shown on when you do a part search into the database, and what is shown on the circuit diagram.
As a rule, only the value should be shown on the circuit by default, and then you should have the option to make further fields visible if they are critical to the application.
The fields that get displayed when you are looking for a part that your company already has in its database (you don't want to use a new part if there is an existing one) should include, as well as tolerance, package size, technology ...
whether it is available from multiple sources, or needs to be from a specific manufacturer
whether there are any gotchas lurking in the datasheet that need to be checked, so a note that Y5U dielectric only supplies 30% of the rated capacitance at rated voltage for instance, or that the power pad must be isolated rather than grounded
whether it's in active production or going obsolete shortly
monthly use, or number of different designs used on. A little used component is a good candidate for future elimination.