How do you create a “minimalistic artistic aesthetic” atmosphere/look on a budget?

I feel that the hardest part about having a minimalistic aesthetic is letting go. By letting go, I mean choosing those Knick knacks that are non essential, and keeping those few items that really matter.
Once you have those items it’s easy to design around them and figure out the mood you wish to have in your space. Is it warm and cozy, or cool and clean etc..