A question regarding airfoil parameters If a hypothetical aircraft, which is a tailless straight flying-wing with no fuselage, has the following characteristics:

moderate forward sweep
an aspect ratio = 9
a dihedral angle of 3 degrees
a slight tapering of 5 degrees on each edge
wing twist (10 degrees of total incidence difference between centreline and wing tip)
positively cambered airfoil at centreline, slightly less at the root, minimally positive camber at the inboard section, symmetrical outboard section, negative camber from there towards the wing tips
thickness 10% at the tips, 15% at the root and 20% at the centerline
a low wing loading, i.e. 50 kg/m2
slightly forward CG

And if the required stability in yaw (proverse yaw) is considered to be ensured through sufficient wing twist and symmetrical airfoil/negative camber at the tips,
what kind of airfoil characteristics - or even better - what specific airfoil examples (or at least, a specific airfoil category) would provide both low induced drag and ample lift ability at low speeds of 50KT, but still have low resistance at higher speeds i.e. at 200 KT?
Specifically, how much camber and reflex camber change (in ratio to symmetrical) should be sought for each of the different segments of the wing centreline, root, outboard section and wingtip?
Or, would it be sufficient if the whole planform has an identitical airfoil shape (scaled for chord length due to taper)?
What would be the Centre of Pressure positions (in chord percentage) of such a wing at slow flight or in high-speed cruise?
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I know it may be a fairly wide question with a myriad of possible answers but I would be grateful to see some examples, so I can have some notion on what the camber/reflex camber for these wing characteristics should be, and to better understand via examples.
Thanks
For a wing to be stable in its own right, its aerodynamic centre must remain static with changes in angle of attack. The usual approach is to sweep the wing and wash-out the outer section. Because your wing is unswept, you have only two choices in creating a stable aerofoil:

A symmetrical aerofoil, i.e. with zero camber.
A cambered aerofoil with reflex camber towards the trailing edge.

The first of these has poor low-speed characteristics and has really only seen use on aerobatic and early supersonic types.
The reflex type offers better low-speed characteristics, thanks to its positively cambered leading edge. RAF 34 provides a good example; it was developed in the 1920s when RAF 33, with even greater reflex, was found to have high drag. RAF 34 had much better performance above 200 kt and was used on several tailless types (usually swept and washed-out as well) such as the Westland Pterodactyls. It would be a good starting-point for your search.
But be aware that your tapered &quot;plank&quot; wing will have abysmal handling characteristics and a vicious, unrecoverable stall. Washout can help a little here, and the CG position will depend on this, as well of course as on your chosen aerofoil. Maybe using it as a hang-glider might be tenable, as the pendulum stability will mask the worst handling issues, but I would not want to take it up in case it stalled!
Addendum
Some remarks have touched on the NASA Prandtl-D experiments led by Albion Bowers, which owe much to Prandtl's &quot;bell-shaped&quot; lift distribution and Reimar Horten's exploitation of it in his flying wings. Prandtl's analysis applied principally to the straight wing and was not concerned with stability or yaw. By contrast the Horten/NASA implementation is applied exclusively to tailless swept flying wings, where stability and proverse yaw in the turn are essential to docile handling. In this latter context, many subtle variations of aerofoil across the span have been tried over the years. JW Dunne anticipated it all, and more, intuitively back in the pioneer era - the Science Museum archive contains boxfuls of his research models - but he was no mathematician. The precise relationships between the various design features and resultant flying characteristics still remain somewhat clouded and contentious, and Dunne's work studiously ignored, so some aspects of the original question here remain unanswerable. But one thing everybody I have mentioned has agreed on; if you do not sweep your wing then you are making life much harder for yourself.