Dailies & Weeklies
Every Monday between 6-7am EST the weeklies reset. Be sure to complete as many of these as possible. It's easier to find successful carry groups early in the week since many of the strong dedicated players burn through weekly content on Monday/Tuesday.
Note that several shops sell limited quantities of goods every week with increasing costs so if you can't afford to buy all of it that's ok. Things like Oracle Dust, Oracle Crystals, and Ancient Relic Dust becomes extremely expensive and are probably not worth all that Zeny early on so buying a few every week is probably a better move. Focus on the materials you need the most at the time.
Note, underlined entries are links to pages discussing that content...
Events
Kafra Girls / Cat UFO (Wednesday's Only)
MVP Battle (Friday's Only)
War of Emperium (Thursdays)
War of Crystal (WoC) (Sundays)
Shops with Weekly Limits or that Change Weekly
Lucky Coin x15
Although marshmallows no longer reset every week the headwear cycles out so make sure you check this before week's end!
Oracle Dust
Oracle Crystal
Enchanting Crystals
Ancient Relic Shop in Prontera
Svartalf Normal Dust (Relic Dust)
Faint Rune Stone x10 (green runes)
Smooth Rune Stone x3 (blue runes)
Sealed Rune Packs (small runes, important in the long run since you upgrade these and they affect hard to find stats like Pen)
Honorary Shop in Prontera (costs Honor Proof, skip this shop if you can't buy all your praying card packs)
Mora Coin x40
Gold Medal x7
Contribution x7
Brave's Holy Emblem Shop (Echoing Corridor items)
Glittering Star Rune x2
Light Extract Crystal x10
Various other limited items such as sealed rune packs, praying card packs, and more. Star runes and extract crystals are a higher priority here.
Crystal of Chaos Shop (Maple Leaf/Frost Domain loot)
Nightmare Chest x10
Svartalf Elf Dust
Super Screws (to craft ancient gear)
Sealed Rune Packs (Small Runes)
Mora Coins
Gold Medals
Contribution
Glittering Rune Stones (S Rune)
Daily Tasks
Always keep up with any events that are in progress. They always offer unique headwears as well as praying card packs, runes, and other useful stuff!
Do any all event dailies you can find (always top priotity!)
Do up to three rift challenges if you still need low level Ancient Equipment
Claim your pet labor rewards before they reach the cap for each shop
Check the lucky shop for deals if you have excess Eden Coin
Do Hunting Grounds dailies for your 4 ancient equipment coins if you have access
Do daily Singra Box quests if you haven't done them all yet
Lighthalzen Singra Box
Louyand Singra Box
Eclage Singra Box
Comodo Singra Bottles (yes, they are just bottles lying on the beach)
There may be a few more things I've missed but this should be most of it.