[RPG] When a cleric not devoted to a deity picks the domain War, can he pick any weapon

A cleric can opt "to have no deity" yet such a cleric still "select[s] two domains to represent his spiritual inclinations and abilities" (Player's Handbook 32). If such a cleric picks the domain War (PH 189), the cleric receives the domain's granted power: the feat Martial Weapon Proficiency (PH 97) with the cleric's deity's favored weapon (the text parenthetically noting if necessary) and the feat Weapon Focus (PH 101) for that deity's favored weapon.

Can such a spiritually inclined cleric pick any weapon as this favored weapon—even an exotic or simple weapon—or must the weapon picked be a martial weapon? If the cleric can pick any weapon, if the weapon's exotic or simple, does the cleric forsake the domain-granted feat Martial Weapon Proficiency yet still receive the domain-granted feat Weapon Focus for the weapon? Finally, is there any special dispensation for picking as this favored weapon the unarmed strike or a natural weapon? (This last closely related to this question.)

As an aside—and to demonstrate the ripples an answer sends throughout the game—some published deities grant their clerics access to the domain War and have favored weapons that are exotic weapons: for example, Eberron Campaign Setting's the Mockery and the kama; Player's Guide to Eberron's Spirits of the Past and the double scimitar (presumably shorthand for the Valenar double scimitar rather than intended to be the Arms and Equipment Guide's double scimitar, but whatever); and Serpent Kingdom's Parrafaire and the tail scythe (really whatever). Is it safe to assume what occurs with the War domain's feats when a spiritually inclined cleric picks the domain War and picks an exotic weapon also occurs to clerics of such deities when such clerics pick the War domain?

Note: I'm probably way late to this party, but on behalf of one of my players (okay, fine, yes and myself) I'm assembling a list of domains and, subsequently, gods, yet texts don't seem to address to this issue. I suspect it's long since settled somehow somewhere, but so far—after digging around in the final 20 or so books published for the game by Wizards of the Coast (I start my research at the end and work backward)—an answer eludes me.