Mythic+ will scale from ilvl 236 (+0) to ilvl 262 (+14). These pieces will be able to be upgraded to item level 272 with Valor once you have KSM. Your weekly vault will contain an ilvl 278 piece as long as you complete +15’s or higher. During the first week of Season 3, end of dungeon loot will be capped at +10 which is ilvl 255. When you get your first season 3 vault on the first week of Mythic, your vault can award up to a 278 item.
Raid gear drops 252/259 on Normal, 265/272 on Heroic, and 278/285 on Mythic. Normal will be useful the first couple weeks to get specific trinkets and set bonuses. The ilvl from +14’s will outweigh almost all gains from Normal raid outside of these pieces.
This means spamming m+ for the first few weeks will be the best way to get gear. You can get to an average ilvl of 262 and have items ready to upgrade with valor. Getting 4 or 10 +15’s in a week increases your chance that a good piece of loot will come at 278 so that you’re prepared for mythic raiding.
Until you have access to the Creation Catalyst, you should not pick a non-set item in a set item slot from your weekly vault.