Would State court would have jurisdiction before the Feds?
No. It's clearly a federal reservation - federal property. It's complicated and there are some limited circumstances where a murder on a base could be prosecuted under state law, but this case isn't one of those cases. The military will get first crack, then the feds if Obama - and it would be Obama's decision, decides to move it to federal court.
I would very surprised if he wasn't prosecuted under the UCMJ. What will be interesting will come at the conclusion of the trial and after the exhaustion of appeals - which will take 12-36 months. Unlike a civilian federal case where the death penalty is sought, in a military dp case, the CIC will actually sign the condemned death warrant. IOW, Obama will have to physically sign a document ordering his execution. That should make for a challenging political decision for Obama.