Say a runner runs on a remote server protected by Hudson, and they are limited to a single-card access. Between the two cards available are an upgrade with a high trash-cost, and an agenda. They choose the facedown upgrade and cannot afford to trash, and I have chosen not to rez.

When the upgrade is returned facedown, do they now have the benefit of knowing which of the two cards is an upgrade, or do I have the choice or re-arranging the cards in the remote server?

This is in the FAQ:

Can the Corp rearrange his installed cards within a single server, to obscure the order that he installed them in?

The Corp must keep the order of his installs clear to the Runner; he cannot rearrange cards in servers however he likes.

EDIT: Whoops. Redundant post. I referenced the same question in the FAQ.

Thank you Grimwalker.

As an additional Q along the same lines (Hudson fascinates me), if the Runner has his choice between three-four cards and indicates one that is an agenda, do I then have an open window to rez Ash, Red Herrings, etc. before the access or must I rez before the choice is made?

The last opportunity to rez cards would be step 4.3 before the run is declared successful and the Runner starts their access (the FAQ has a detailed timing diagram for turns and runs on its last two pages).

Thank you kindly! My FAQ isn't handy and the PDF is miserable to hunt through on this computer. Much appreciated folks! :-)