In my opinion, two-handed works best in pvp. Make sure you use the right glyphs, for example 'Anti-Magic Shell' and useful talents include 'On A Pale Horse' and 'Improved Unholy Presence'.
Personally, I've done better with a Frost spec in PvP but provided you use the right spell rotation, you should do fine with Unholy.
Hope that helps.
Since you're a DPS you should get these:
Polished Spaulders of Valor
Polished Breastplate of valor
Worn Stoneskin Gargoyle Cape
Polished Helm of Valor
You can get the first two with Justice Points in Orgrimmar/Stormwind from the Justice Heirloom vendor or in Dalaran from the Heirloom vendors.
The cape and the helm are available from the Guild vendor once your guild has reached a high enough level (10 for the cape, 20 for the helm)
Adding a Bloodied Arcanite Reaper to the mix may be a good idea: it may lack the experience bonus, but you get a good weapon that scales with your level.
All of the above would provide you a nice 35% bonus experience (until level 80, at which point spaulders and chestplate stop to work) and a good boost to your stats, scaling gracefully while you level.
If you still have Justice points in excess you can also get the Swift Hand of Justice: not a great improvement when compared to the other heirlooms, but a little haste and a self heal can help from time to time.
As Adanion pointed out in the comments an alternative way to get your Heirlooms is from Dame Evniki Kapsalis at the Argent Tournament.
You'll need Champion's Seals to buy items from her, which are a reward from the dailies in the zone.
This area is not current content anymore, since it's been released in Wrath of the Lich King, and it takes days of work to unlock all of the dailies available.
It can be anyway a good source if you have nothing to do except waiting for the next Heroic to pop up. In the event you already unlocked the Tournament and you have many 80+ character it can even become quite profitable, since Heirlooms are bound to account and you can move them between your toons.
Best Answer
You can basically just buy the heirlooms that have useful stats for your class. A thing to note:
Mail with Agility/Intellect and Plate with Strength/Intellect will change the armor type pre level 40
This means for Hunters and Shamans you can buy the Agility-Mail for example. They are Leather under level 40 and turn into Mail automatically once you reach level 40 with your character. (If you send it to another character that's lower than 40 you will get leather again). This of course works the same for Plate wearers.
Heirloom armors like the Agility-Leather however will not turn into mail after level 40.
You also have to know that the main reason why you actually buy heirlooms is not the fact that they scale with level, but rather for the Percentage bonus experience. This means you can also buy a Agility-Leather armor on Hunters or shamans for example. While you can also play with Cloth-Intellect on a warrior during the first few levels if you don't have the plate set, you should definitely switch to normal armor after around level 20 since it would take you too long to kill NPCs after this point.