DPI is a non sequitur in video graphics post, however if you're using an application that is asking for a DPI reference for it's page size setup try to either diver it into pixel mode or if it's still asking for values 72 or 300 is a safe bet. (You can only use it in reference to a monitor or a camera sensor) as in something that could actually be measured in inches, indicating its pixel density per inch. DPI = Dots Per Inch.
While you're at it, goole "pixel aspect" as not all pixels in video are square.
There is the pixel aspect ratio that you need to take into consideration. NTSC DVD is 720x480 in both 4:3 and 16:9. I set my canvas in Photoshop in 720x480 and select the correct pixel aspect ratio (1:0.9 for 4:3, 1:1.2 for 16:9). In that case, your image will look correct both in Photoshop and in the final DVD (a circle would be circle, but not ellipse).
Yeah DPI is a tricky thing. It is for print/scan material. For video it's the screen size/resolution that counts.
I'm now thinking, if picking 1 dpi or 72 dpi makes no difference, then why don't pick a higher DPI canvas in case that art work need to be printed, or use with other printing material?