So you want the finished edge of the door to look like:
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You can do either, it will depend a little on the type of bit you are going to use, and how you want to guide the router. Working with the router against the flat of the door however will tend to give a more stable platform to balance on.
A bearing guided cutter will ultimately follow a straight edge and guide the router. This is simpler to use than using a separate guide rail usually.
So with the router above, base pointing toward the flat face of the door, and a bearing guided rebate bit, you set the depth of the bit using the plunge mechanism on the router and lock it in position:
Then keep taking further passes, until on the final pass, the bearing is in contact with the lower thickness of the door, and produces a dead straight cut on the top surface (as long as the edge of the door is also dead straight!)
If your rebate cutter will also cut on the under surface (i.e. the side where the bearing is) then you could approach from the other direction, by doing a shallow full width cut and then plunging deeper into the work on each pass.
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