Use 720 x 480 for SD.

720x480 for standard 4:3 SD is what I used to use.  But this one was filmed in 16:9  I was told to use 704x480 for the video to avoid black bars.  So I'm trying to understand what size to make my PSD file from photoshop for the menu, 873x480, or 720x480?

It is the same resolution in 16:9. Photoshop has a preview mode that corrects the aspect while designing the menu. Use that for best results. You can design in 873x480, but you still need to save it as 720 x 480.  You do not need to worry about the black bars showing up. This only happens when rendering in Vegas, not DVDA.

So should I just do it like this? 

Change the pixel aspect ratio if you are doing 16 x 9, otherwise, yes.

To D1/DV NTSC Widescreen 1.21  correct?

Correct.

Unfortunately Vegas Pro / DVD Architect unable to read the pixel aspect ratio correctly.

First time I migrate from Adobe Audition to DVD Architect, I had similar confusing issue of 'weird non-standard resolution' for still images authoring.

My PAL Widescreen with Aspect Ratio of 1.000 is equivalent to 1024x576 in Adobe's world. But as DVD Architect's help says, you're recommended to make the image at size 1049x576.

So in photoshop, I choose template widescreen Square pixel, then image resize it.

In your case, select NTSC D1 Widescreen Square Pixel with 864x486 size, then custom resize it to 873x480.

I have make this steps as macro.

There is no pixel aspect in a still menu for DVDA to read. It plays the menu back at the project and/or player settings. I have never had a problem with a menu I created at 720 x 480 (using the aspect preview correction in photoshop). If you give any other resolution to DVDA, it will have to resize it. But I am in the NTSC format, so I can't vouch for PAL and any errors DVDA might have handling that. (isn't Adobe Audition an audio program?)

Ok, so when I make a new file at 720x480 with the PAR set to D1/DV NTSC Widescreen 1.21, it looks wide in photoshop.  When I save it, I get just a regular 720x480 file.  So why do I even need to select the PAR of D1/DV NTSC Widescreen 1.21 in the first place?

Because if you design it at 4/3 aspect the image will look right in photoshop but be stretched horizontally.  If you design it for 16:9 at the correct aspect, when it is displayed as 16:9 on a DVD, it will be correct.  If you do not design it at the correct aspect, it will be stretched when viewed.  But NTSC DVDs are always 720 x 480 (or 704 x 480) resolution. It is just the aspect ratio that is changed upon display. they are called non-square pixels. Photoshop has just created a way for you to work in normal 720 x 480 but view in widescreen while designing. You could create an image at 873 x 480 and then resize it to 720 x 480 when saving and the result will be the same. But you have to remember to resize it. With the Photoshop aspect correction, you don't have to worry about resizing. IF you look at the 720 x 480 file created with widescreen on its normal resolution square pixels, it will looked compressed.

Ok, starting to make sense now.. And I guess since most TVs aren't CRT, that I don't have to worry about safe areas, correct?

Yeah, for the most part, safe areas are a thing of the past. although I have found a few TVs still cut off at bottom and top.. Just not as much as it used to.