Sidequests restart, but in the bombers' notebook you still have marks for the ones you've completed.
Things that are saved: masks, c button items (as well as sword/shield upgrades but not items you get as part of a sidequest which show up on the far right of the subscreen), dungeon maps/compasses, pieces of heart, ocarina songs, and boss remains
Things that are lost: small keys, boss keys, ammo/supplies/rupees, and stray fairies.
With the c button thing I mean that things like the Moon's Tear are lost but an item like the bow you would keep. You'll figure it out eventually and never have to think twice about what's saved and what's lost.
In terms of main quest progress the areas outside of dungeons reset as do the keys and doors inside the dungeons. Most of the quests leading to dungeons result in obtaining a song so once you get the song you never have to repeat the area leading up to a dungeon again if you want to return to the dungeon. Once you get the map, compass, dungeon item, or boss remains you never lose them.
Also never forget to put rupees in the bank as that's how you can avoid losing them.