Here are the visual effects of these options, they only come into play if the object you are applying the drop shadow has another transparent effect applied.

For some reason tears ago I was having problem with appiling drop shadows and other effects and it was looking screwy when it printed. Someone said to make a different setting in the "Transparency Flattener Presets" dialog box.

Transparent pages always get flattened when you print, and usually you can control how the flattening happens from the Advanced tab by picking a preset.

When you export a PDF transparency gets flattened when you choose PDF 1.3 from the Compatibility popup in General. So, the PDF/X-1a standard is flattened by you , while the PDF/X-4 standard postpones flattening until the PDF is printed.

99% of the time the default high resolution flattener preset will be fine—if you had a lot of very small type on a transparent page you might need a text resolution higher than 1200.

If you export your own transparency it's easy enough to look at the quality in Acrobat. Here's an exaggerated low res flattener where I've forced the text to rasterize vs. the default high res:

it looks like I'm screwed as far as applying the drop shadow in InDesign.

Keep in mind this is simply a preview change the output numbers are not affected—when you add transparency the document's CMYK profile is always used to display black values. The output gray values are not changing.

I don't have a clue want to pick.

The accuracy of your CMYK preview depends on the accuracy of the document's assigned CMYK profile and your system's moniter profile. So if your only concern is matching the preview of a grayscale in PS and ID, pick your ID document's CMYK profile (see Edit>Assign Profiles...) from your system's profile folder.

But I came across this. I went to View>Proof Setup>Custom and picked "Generic CMYK"

Proof Setup shows you what will happen if you convert to the setup profile sometime in the future, so it's not helpful because you won't be converting to Generic CMYK.

What system are you using and what't your ID document's CMYK profile? You can check the doc profile by choosing Edit>Assign Profiles...

Do I now need to do a "Covert to Profile" to all my Grayscale images before bringing them into InDesign, or just leave them alone?

Convert to Profile is not an option if you want to use a CMYK profile as the Gray space. If you use a CMYK profile as the destination when you convert to profile the mode will change to CMYK, so you definately do not want to do that.

Loading a CMYK profile as the Gray working space simply previews the gray values as they would print on the black plate of the CMYK press printing to the chosen profile's spec's.

Not sure where Separation Preview is in ID.

Window>Output>Separations Preview

The Adobe recommended profiles should be here:

System/Library/Application Support/Adobe/Color/Profiles

But profiles can also be in:

Users/user/Library/ColorSync/

System/Library/ColorSync/Profiles

The CMYK Profile is set on "U.S. Web Coated (SWOP) v2" in the Assign Profiles dialog box. Should that be changed?

What kind of press will print the project?

Is there an Application Support folder in your Sytem

/Library/Application Support/Adobe/Color/Profiles/Recommended

POD halftone quality is marginal, so don't expect much. You should be able to order a sample at little cost.

US SWOP or US Sheetfed.

When I do find out, what are the steps I need ot change the icc?

In ID you choose Edit>Assign Profiles>Assign CMYK Profile and choose from the pop-up

In PS you load the profile as per Peter's instructions,and then you also have to make sure the working Gray space you've loaded is assigned to the grayscale image—that's Edit>Assign Profile>choose Working Gray.

I liked the days when I had a soft proof done and I calibrated my monitor to it.

There's nothing stopping you from doing that now, but it would only work if you were always preparing jobs for one press. If you had three jobs, one for sheetfed coated, one for a web press, and one for news print, you'd quickly run into a mess because you'd have to change the profile of your monitor every time you worked on a file—those three press conditions will produce different color from the same values.

CMYK profiles also have some subtlties that you can't acheive by adjusting your monitor. Modern profiles will show the difference between blacks with different amounts of CMY in them, or different ink sets—no amount of monitor adjusting will show those differences.

Here are different blacks for uncoated. The preview shows what would happen on press with different CMY amounts. This is why ID flattens out your grayscales because black only on press is never absolute black:

So if I have to set my monitor to a setting that works close enough for this book I'm working on now, that would be fine for me.

You don't have to adjust your monitor. For grayscales there is Custom Dot Gain which gives you a curve dialog that allows you to adjust the display of grayscales with out changing the output numbers (Color Setting>Gray>Custom Dot Gain...):

If you adjust your monitor without creating a new monitor profile it will generally break color management in all of the Adobe apps.