What gear should a level 80 assassination rogue need to acquire for both PvE and PvP?

Answer 1

PvE Starting Kit

Craftables

Bladeborn Leggings, Footpads of Impending Death (Ilevel 265)

Knightbane Carapace, Bracers of Swift Death (iLevel 265)

Death-warmed Belt (iLevel 226)

BoE from the Auction House

Ikifirus' Sack of Wonder (iLevel 265, ICC) - replaces Knightbane Carapace

As for weapons, starting items like the SuperNumary Sticker are good starter items, or even weapons bought from Reputation Vendors or quest rewards. From here on, the best option is to run heroics to replace all lower-level items and get some decent trinkets. After a bit of time, use Emblems of Triumph and Emblems of Frost to replace any lower-level items you can, or slots for which no good item dropped.

Priority should be to get your Tier-10 gear from the vendor, buying Shoulders and Helm items first because they are the hardest to acquire. After that, go for a good trinket.

PvP Starting Kit

For the PvP Starting Kit, the best you can get is the Relentless Gladiator's kit, which can be bought using Emblems of Frost or Honor. You can also get a good set of shoulders from the Wintergrasp Vendors for Marks of Wintergrasp. The first buy should be a Medallion of the Alliance, for the Resilience and get-out-jail free card (unless you are a Human).

Your best bet will be to run Wintergrasp and do the weekly quests for it anytime you can, and save up for more pieces. Wintergrasp is massive and you can find safety in numbers, picking off stragglers as you go.

You might not even need good PvP gear, but if you want to feel safe have a Leatherworker craft Eviscerator's Chestguard, Facemask, Shoulderguard, Waistguards, Treads and Legguards for a Resilience buffer and good starting stats.