DPS Stats
The absolute most important stat for any DPS Death Knight is Strength. Strength effects how hard a Death Knight can hit, and it scales with various talents and buffs. As a general rule, Strength is always more important than Attack Power, even though they appear to be, essentially, the same thing. It is also vitally important for Death Knights to have the appropriate amount of hit rating. All two-handed melee DPS classes need to have an 8% additional chance to hit before they cannot possibly hit their target any more often. Additionally, there is a measure of expertise required for the same reason. Death Knight DPS that attack from behind a raid boss need only 26 expertise. Besides Strength, and its close companion Attack Power, DPS Death Knights also favor Agility. While nowhere near as good as Strength, Agility provies buff-scaleable critical strike chance.
Tank Stats
Death Knight tank stats look a lot like other tank stats, with the exception of block chance/value (seeing as that DKs have no shield to block with). Death Knights are much more damage mitigation than they are avoidance, because of this. When looking for gear upgrades, Death Knight tanks need to min/max. The Defense cap for a level 80 Death Knight is 540. Any amount of Defense above that is wasted, however, the Death Knight should never sink below this mark. After maintaining the Defense cap, Death Knight tanks should focus on gear that gives additional Stamina, Armor, Dodge, Parry, and Strength - in that order. Parry has a much worse diminishing return than Dodge. This means that as you gain parry it takes more and more rating to equal 1% of parry. This means that, generally speaking, 15 Dodge is going to be much better than 15 Parry.
PvP gear can be obtained in a variety of ways - all of which require you to actively engage in PvP. You can get honor through Battlegrounds, daily quests, and Wintergrasp which can be used to purchase superior and epic PvP items. Additionally, you can obtain these items from Wintergrasp vendors or bosses. You can also choose to do Arena, and if your team is good enough, earn some of the best PvP items in the game. For more information about getting PvP gear for your new 80, please see the PvP Gear Guide section of the article linked here.