units selection for patrolling

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1) The manual does not document the unit costs.

The numbers for initial gold cost can be found at the wiki
http://dom3.servegame.com/wiki/Main_Page or in Edi's DB (see his .sig)

Upkeep is the initial gold cost of the unit divided by 15 for non-sacred units, or initial gold cost divided by 30 for sacred units. This applies even if you did not pay the initial gold cost (eg. because you summoned instead of recruited a unit).

2) I don't think the manual gives a formula for unrest reduction through patrolling, it just gives a destealth formula.

I usually patrol with free militia, slaves if I've got them, or tribal/monkey archers. Archers will do a pretty good job of killing barbarians at the same time they patrol, and they might be able to join up with your army if you need them in a pinch.

Edit: Lingchih's right about flying units. But there's not a lot of nations with cheap flying base units, maybe just Pan and Caelum?