As Tamas Papp has explained also, I agree that the answer to your question will probably not be based on something which already exists. Since you intend on becoming a user of Julia, your needs will arise out of pursuing problems which have not already been solved efficiently previously. When we decide to do some programming with a language, we typically wish to achieve something that has not already been done before, and in trying to achieve that goal you will have various changing requirements for what you need to import from previously existing code.
In many cases, I have been able to achieve my goals by only using the Base julia language, since I try to use as few dependencies as possible to achieve my goals. However, as a mathematician, I find several basic packages useful such as
Typically, the packages I like to use the most often are the ones I’m currently developing and building up.
However, I think often times the base Julia language itself often provides most of what is needed. Also, my list is probably not that relevant to everyone. So I would focus on finding a feasible unsolved problem first when trying to create something from scratch, and then searching online for special purpose methods to fill in the gaps provided by other packages.
Julia is considered a general purpose programming language, so a set of standard packages considered useful to one person might be completely different from the needs of other people.
For example, many people talk about
DataFrames, but I don’t care about them at all.
Just go on github and click on what interests you or solves your problem, I always open tons of github pages.