Magic items are definitely rare in 5e, they aren't even priced (they occur in the DMG and are also scattered about the published adventures). They are meant to be special by their rarity (from my experience, by level 6, each player should have at least 1, probably 2 or 3). By the rules, they aren't purchasable like in 3.5 or Pathfinder (where magic item shops are relatively common). That said, I'm sure the DMG, which is loaded with variant rules, has suggestions for running a game with high magic item frequency.
Like magic items in most games, they vary dramatically in their internal rules - while most that you've seen are 1 or 2 use per short rest, some are per encounter, some are per day.. wands and staves are interesting in that they are filled with charges that replenish at a semi-random fixed rate per day, but it's up to the player how they manage the charges.
13th age expects players to gain more magic items than they have levels (otherwise the really cute magic item personality rule never comes into effect). It's like this, each magic item has a 'personality influence' (my character has a cloak that boosts intelligence that makes him view himself as superior to those of other races, or something like that - it's been a while since I played him). The personality influence doesn't affect you UNLESS you have more magic items than your level.
