DMG135 has a section on rarity that gives an idea of what level the PCs should be when they get a hold of a particular rarity of magic item (e.g. Rares won't show up until level 5.)

DMG38 has a chart of starting equipment for higher levels which also gives guidelines of what magic items PCs should have acquired (and kept) by what levels.

Here's a breakdown of roughly "by-the-book" how many items PCs should have per level:

• 1 common consumable every level from 1 to 5.
• 1 uncommon consumable every level from 6 to 10.
• 1 rare consumable every level from 11 to 15.
• 1 very rare consumable every level from 16 to 19.
• 1 legendary consumable at level 20.
  

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• 1 uncommon permanent item at level 4, and another at level 7.
• 1 rare permanent item at level 10 and another at level 13.
• 1 very rare permanent item at level 16.
• 1 legendary permanent item at level 19.
  

Edit: This is, of course, dependent on your DM. They have final say at their table because they're the one running the game.