RE: How do I pick a cross section?
I would first look at some of the airfoils available that include a slight amount of reflex in the trailing edge - that is, it appears to have a built-in "up elevon". This will take care of or minimize pitching moment issues. (I am assuming this is a "flying wing" type delta wing, as opposed to a MiG-21 type delta wing, which uses a seperate h-tail for pitch control.) This would give you a clean design.
I'd also look at airfoils used for similar type airplanes, also, to get you started.