For your first Emblem of Heroism purchase, you're going to want to strongly consider grabbing the Mirror of Truth. The chance on critical hit for 1000 attack power is just too delicious to pass up, and it provides a good chunk of critical strike rating to help the proc along as well.
For your other trinket slot, you have a few options. The Sphere of Red Dragon's Blood from Heroic Nexus is a nice hit rating trinket that should free you up to shed some hit rating elsewhere, and it comes with a nice attack power on use ability as well. If you're looking for a straight attack power trinket, you can always grab the Incisor Fragment from King Dred in Heroic Drak'tharon Keep, although the armor penetration on use is strictly lackluster.
If you're incredibly rich or are a scribe with a lot of ink saved up, consider trying to grab the Darkmoon Card: Greatness. The strength version should offer a very nice chunk of attack power. Finally, as a Dark Horse option, there's the Crusader's Locket. Despite being a green quest reward, it does offer one thing: A very high expertise proc. There's very few pre-raid options for a DPS Death Knight to grab Expertise, which means you'll get dodged a decent amount. The expertise proc has a chance at helping that, but only a chance.
For rings, there's not many strength options in 5 mans that aren't tank stat focused, so you'll probably have to settle for attack power. That said, consider grabbing the Hemorrhaging Circle from Heroic Gun'drak. Not only does it have a good amount of agility and attack power, but it also has Expertise, which is in short supply on Death Knight friendly armor in the 5-man game.
For other ring options, the Band of Frosted Thorns is a rare DPS-focused ring that sports strength and critical strike rating, and is a strong choice for a Death Knight. If you're looking for hit rating in a ring, the Mobius Band off Chrono-Lord Epoch is a solid choice. In pinch, you can also grab a Ring of Scarlet Shadows from a Jewelcrafter, which has hit rating and critical strike rating as well as a decent amount of attack power and a gem slot.
In Heroic Utgarde Pinnacle, you can get a good solid Death Knight DPS neck off King Ymiron in the form of the Gold Amulet of Kings, which sports plenty of strength and critical strike rating. Once you have 25 Emblems of Heroism to spare, though, you may want to pick up the Pendant of the Outcast Hero, which has enough attack power to edge out the Gold Amulet of Kings along with a good amount of agility and critical strike rating.
Weaponry, of course, is a sticky subject for a Death Knight, what with the whole Dual Wielding versus 2-hander thing. I myself come down firmly on the 2-hander side of the debate. I don't begrudge people the ability to dual wield, but Death Knights will always be primarily a 2-handed weapon class to me, and will be what I always advocate for. Still, I'm also a class completionist, so I'd be amiss if I didn't have at least a passing familiarity with dual-wield weapon itemization.
For 2-handed weapons, I'd like to refer you to the weapons section of this Lichborne column from a few weeks ago. I myself went with the Titansteel Destroyer, and I do not regret it for a moment. The price wasn't too steep since I supplied the Frozen Orbs myself, and not only does it hit hard, it has plenty of hit rating too.
For Dual Wielding, it's still a bit in flux as to what exactly works. Before 3.0.8, you wanted two fast weapons since your weapons were essentially there to proc Killing Machine as fast as possible. Since 3.0.8, Killing Machine is on a proc per minute basis, so now you probably want a slow main hand in order to get more damage on weapons strikes. You still may want a fast off-hand to proc Blood-Caked Blade faster, though.
As for which blades to wield as a dual wielder, You can grab the Reaper of Dark Souls from Ebon Blade reputation for your main hand. With a nice, slow attack speed and a good chunk of hit rating, which you may want more of than usual if you plan to dual wield, it's hard to beat it in the main hand slot. For your fast offhand, grab The Interrogator from Heroic Oculus, which also has a nice chunk of hit rating along with a blazing fast 1.60 attack speed.
If you want to go the extra mile, you can also pick up some epics for both slots. The Titansteel Bonecrusher is a nice slow weapon that blows the Reaper away on pure DPS. It also has some expertise rating, though it lacks hit rating. It's crafted though, and the mats will probably set you back a few thousand gold. For the offhand, you can grab the Grasscutter for 50 Emblems of Heroism, although again, it has no hit rating to offer despite its superior DPS.