Schmutz, revisited

Another thing: in order to assess your selections, once you are in Quickmask mode, you can go to the Channels panel, and click on the Eye of the composite channel, to see the selection in Black and White mode, before you use levels or treshold.

As an alternative, if you have already converted the selection into a layer mask, ALT+click on the Layer mask thumbnail.

Remember to always look at 100% magnification for accurate assessments.

Edit: a last thing: in the past the default color for the Stroke Layer Style was Red. It was used to quickly find stray pixels. 

Set it to red or magenta, whatever color you do not have in your image, to avoid surprises like those you mentioned in your first and previous posts.

Selections can also, and have for years, be created directly as paths using the pen tool, or, now, you can activate a tool that's in testing mode, if you go to Preferences>Technology Preview and activate the Content-Aware Tracing tool that you will find alongside the pen tool.

Hello, @scotwllm 

If you really want to have black or white edges to your selection, do, as, @Myra Ferguson suggested,

1) Convert the selection in to a Quickmask, by hitting Q.

2) Then, go to Image>Adjustments>Treshold. You'll only have 100% selected or 100% unselected, a stair-stepped, Myes result.

Another way to get a sharp edged selection would be, as @Bojan Živković11378569 hinted, to Convert the selection into a vector mask.

In order to do this, 

1) with an active selection in marching ants mode, open the Paths panel, click on the Make Work Path from Selection, the button in the center that looks like a circle with 4 anchor points.

this way, you get a path from your selection, it only allows selected or unselected. But it works on top of pixels, so there might be aliasing. If the lines are not smooth enough, you can adjust its Tolerance by doing an Alt+click on the icon.

2) Once that path is active, go to your Layers Panel, and CTRL+click (PC) CMD+click (Mac) the Add Layer Mask icon in the layers panel, that then becomes the Add Vector Mask. 

If you are a menu person, go to Layer>Vector Mask>From Path.

3 )In order to invert that Vector Mask (once you've excluded the subject, but you want to work on the image with an inverted selection. Select the Path Selection Tool (the black arrow) and, click on the path to make it active, click, in the Option bar on the Path Operations icon with overlapping squares, and select Substract Front Shape, instead of Exclude Overlapping Shapes.

Given the fact that you work on pixels, and that the vector path does not fit on them, you will have partial selection, and not 100% inverted selection. Notice the featherling slider in the properties panel, and I wish there was an offset slider to expand/contract the path ever so slightly. This is maybe a suggestion you could post.

To make a deep dive into masking I can only recommend "Photoshop Masking and Compositing" by Katrin Eismann.

Even if it is soon 20 years old, the foundational knowledge it brings is not to be dismissed.

5 quick tips for clearn selection edges by Colin Smith: https://www.youtube.com/watch?v=2l2mGFZNtzE

Colin Smith hosted a two part video on compositing on Adobe Live: https://www.youtube.com/watch?v=7kBQvHxf5iE and https://www.youtube.com/watch?v=BkDWBTW-LYg 

I hope this helps you master selections, and makes you posting in the future with the tone of a real mentch.

EDIT:Sorry for the duplicate with @Conrad_C I was typing a long answer, did not notice his!

My favorite way to do this is to convert the selection to a vector mask, because a vector path is a hard line by nature. If you like how it’s done in the demo below, here are the three simple steps:

1. Make the selection any way you want (I used the Object Selection tool).

2. In the Paths panel, click the Make Work Path From Selection button.

3. Choose Layer > Vector Mask > Current Path. This creates a vector mask from the path currently selected in the Paths panel. Everything outside the path is totally masked out. The vector mask can be hidden or revealed (Shift-click) in the same way as a pixel layer mask.

The rest of the demo shows how you can edit this hard line using any path editing tools, such as the Direct Selection tool.

Like the ants stopped marching and they turned into a solid line?

There isnt feature in Ps nor in preferences to see selection created using selection tools as solid line. The only way that I know is to use Pen tool to draw path then to turn path to vector mask or guess what? Marching ants.

I want to save the selection and its contents.

Not sure what exactly you want. There is option to save selection using Selection > Save Selection but you must have active selection in Photoshop. Contents? To save selection and what is selected? To save selected pixels inside selection? Where to save and for what purpose? If you mean to save selection and content inside selection as we save brush or pattern from menu then to load later in any file then its not available, at least to my knowledge. 

If I inverted the selection and deleted, I want everything else on the layer gone

That should happen, if not please post screenshot of Photoshop window with Layers panel expanded and visible.

Regardless of how the selection was made, if you wanted to make a hard edge with any selection, you could do the following:

1. Switch to Quick Mask Mode (Select > Edit in Quick Mask Mode or press the keyboard shortcut Q) so that the marching ants turn into a red area that's not selected and a white area that is selected with possible feathering in between.
2. Go to Image > Adjustments > Levels and drag the sliders under the histogram to increase the contrast as much as possible.
3. Toggle off Quick Mask Mode by either going back to Select > Edit in Quick Mask Mode or pressing the keyboard shortcut Q again.