You'll find the current rules for
DKoK in
Imperial Armor Index: Astra Militarum . I'd also buy the Astra Militarum Codex.
There are some things you should consider before you get started with Death Korps:
1. Forgeworld has made vague promises to update the
DKoK rules. We have no idea when that will be or what those updates will look like so advice that you get here right now might not be the same advice you'd get after the update.
2. Most
DKoK players would probably agree that the rules for the army aren't as optimized or even as fluffy as they could be. For example, we don't have any doctrines. Instead, we have special rules that we pay points for. We also don't have access to all of the artillery or vehicle options that any other regiment does, which is weird for Death Korps. To get around this, some people run their
DKoK models in multiple detachments, each with a different regiment. So, for example, I run a Valhallan detachment filled with regular Astra Militarum units like infantry squads, Leman Russes, and artillery and then I run a
DKoK detachment with specific
DKoK units like Death Riders and Engineers. This way, I get access to units that
DKoK normally don't get access to (for some reason)
and the cool
DKoK fluffy units that I like. If you do this, just make sure it's really clear which unit is in which detachment and I'd advise not using the same type of unit in multiple detachments to avoid confusion.
As far suggestions for a good backbone to your
DKoK force: Marshal Karis Venner is great (most people use the Marshal model that comes in the Command
HQ squad). Leman Russes always do work - I like Punishers and Executioners. Death Riders are excellent for killing elite infantry with multiple wounds or bullying backlines. Heavy weapons squads are excellent - mortar squads are stupid cheap and a lot of them working together will do a ton of damage to infantry. Lascannons are also a great choice. Make sure to also get yourself a solid amount of infantry - I usually run at least 3 squads. I also like Hades Breaching Drills for the fun factor, but
YMMV.
Hope that helps!