Alright, I'm going to try to document the things that can affect printing, particularly with the Check-In interface, and we'll see if we can come up with ways to make it better. I'm going with trunk/rel_2_1 as my point of reference.
First, we have Admin->Workstation Administration->Printer Settings Editor. Stock Evergreen uses the "Default" printer role for hold and transit slips, though at least one library has customized this to use "Receipt" instead. Slips may be worthy of their own printer role, if we want to make one.
If the default Mozilla Print strategy is used, then in general, a print dialog will appear when printing, asking for a specific printer to use, but defaulting to the one configured through Set Default Printer and Print Test Page. The checkbox option Print silently when using Mozilla Print will suppress this sort of printer selection dialog.
Now, in Circulation->Check In Items, when an item is scanned that desires a slip to be printed, by default it will spawn a dialog with a picture of a turtle and the options Print and Do Not Print. The option Checkin Modifiers->Suppress Holds and Transits will only affect this by virtue of preventing the creation of transits and/or giving items a status of On Hold Shelf. If an item is already in transit or on the hold shelf, the turtle dialog will still appear.
The option Checkin Modifiers->Auto-Print Hold and Transit Slips will suppress the turtle dialog, with subsequent behavior being as if Print had been selected.
In the past, Print (and Auto-Print) would silently print the slip without further prompting for the specific printer to use, but when these slips became templated, this changed. It took a while for this regression to be noticed, and my gut reaction was to add a Printer Prompt checkbox to the interface, to accommodate folks already used to the new behavior. However, there is a good argument for restoring the original behavior (that of always suppressing the printer selection dialog without the need of yet another UI widget) here: https://bugs.launchpad.net/evergreen/+bug/781305
If we do decide to keep the Printer Prompt checkbox, we may wish to disable it if the Print silently when using Mozilla Print setting is in effect, or indeed, if Mozilla Print is not the print strategy in use.
Further complicating printing in the Check In interface is the library setting "Disable Automatic Print Attempt Type List", which can be found in Admin->Local Administration->Library Settings Editor, but which also has a dedicated interface under Admin->Local Administration->'Do Not Attempt Auto-Print' Setting. With this setting, if "Hold Slip", "Transit Slip", and/or "Hold/Transit Slip" is listed, then the turtle dialog is effectively suppressed (depending on the type of slip), but with the subsequent behavior being as if No Print had been selected from the turtle dialog. The context org for this setting is the workstation library, not the transit destination.