There is a really big division here, between older DVD players before HDTV, and with the new system of Blu-ray DVD players for HDTV.
Old DVD players can show JPG image files on the TV from a regular data CDR disk. See your DVD player's manual about showing JPG images, for the media disk types it will play, and how many JPG files on the media that it can show. The DVD player will show any size of JPG image given to it.
HOWEVER, an old style standard DVD player can only output the old Standard TV signal (not HDTV), so the old player must resample too-large images to be no larger than about 640x480 pixels. Any larger images sized for HDTV will be resampled smaller, and shown at low definition (by this old standard definition DVD player).
Images sized for HDTV requires Blu-ray players, Blu-ray burners, and Blu-ray DVD media. Times have changed.
However, many HD television sets now (above Economy models) have a USB port, and a flash memory card can very conveniently show High Def slide shows that way... Plug in the memory stick and the TV will pop up a menu to show JPG files directly, individually or in an automated slide show fashion.
The HDTV USB port does NOT show movie files (at least none I have seen). Creating a Blu-ray DVD would, or a good way to show movie files from a memory stick is to use a HDMI streaming player (like Roku) that has a USB port (shows JPG files there too).
Copy the JPG files to the memory card, just plug the card into the TV USB port, and it can show HD files, not limited in the way old standard DVD players are limited. The thumbdrive-type "flash drives" seem most convenient, but a camera memory card in a reader with a cable works fine too. Just plug it in, and the HDTV senses it and provides a play menu. Or, Blue Ray (and superseded HD DVD) players and recorders exist now, and if you have one, then 1280x720 or 1920x1080 pixel image size fits the HD screen size of course. You can provide any larger size image, but it has to be resampled to fit on the screen, which takes a little time, can run slow. You probably want to size a copy of your images for the screen presentation. 1920x1080 pixel images will show fine on a 1280x720 pixel screen, but huge camera size images can be rather slow.
Again, TV screens are dimensioned in pixels, and images are dimensioned in pixels, so you can realize the connection there. You probably want to pay attention to your TV size when creating the images for this purpose. HDTV screens are mostly either 1920x1080 pixels, or 1280x720 pixels. Some HD monitors have been 1366x768 pixels. Again, images sized for 1920x1080 pixels will show fine on any of these, if that might be a goal.
Most scanner software shows an "Output" dimension, where it shows the size of the image you are creating. If you specify that it should show this Output size in Pixel units (instead of inches), then you can see before how it is going to fit on your HDTV screen size. One way is to just adjust the scanning resolution field (at 100% scale factor) to create the size you want seen there. The way this works is, if you scan 4x6 inches at 300 dpi, you will create (4x300 x 6x300) = 1200x1800 pixels. FWIW, this is just right to print original size 4x6 inches at 300 dpi. It is only a bit larger than HD 1080 pixel screens, so it will show well there too. I would suggest this may be the easy way, if scanning 4x6 inches. Prints larger than 4x6 inches will want lower scan resolution than 300 dpi. Prints smaller than 4x6 can use higher resolution, but again, the target goal is about the TV screen size.
All that seems obvious, and the rest this page is instead about standard DVD players (not about HDTV).
NTSC television is analog (before HDTV), but these 480 lines are correctly matched digitally by 480 pixels vertically. More cannot help. The TV aspect ratio (shape) is 4:3, so it is matched by 480 x 4/3 = 640 pixels horizontally. This is also the origin of the computer VGA 640x480 pixel screen size.
Europe, Australia, and much of the rest of the world use PAL television systems (French SECAM is essentially the same) with a higher resolution of 625 lines, with 576 lines being visible, so the 4:3 number is 768x576 pixels for PAL systems. PAL users should always substitute their own 768x576 numbers here.
For HDTV sets, don't use the DVD player Just put your camera's memory card in a card reader, and connect it to the HDTV with a USB cable (these must be JPG images). For any repeated display, you might first resample the images to HD size to match your TV set, either 1280x720 or 1920x1080 pixels (and then sharpen modestly after resample).
To use a standard DVD player, you could make your JPG images be 1280x720 pixels now, ready for a HD DVD player, but today, that will show 16:9 and operate slower. Or you could just plan to rerun the resample batch again then, to recreate the right size image when the time comes.
For standard DVD players (not HD), the "correct" image size is 640x480 pixels (disputed in the next paragraph). The idea is to make your image size fit within 640x480 pixels for the television screen. Regardless of your TV type or size, this is all the standard DVD player can do. Those are the maximum useful dimensions for standard DVD players, which must resample any larger image to this smaller size.
That is the theory, but in practice, the standard television sets intentionally show an oversize image, extending the image offscreen at the sides, called overscanning (to be sure we never see the edges). The television show creators know not to put anything important near the side edges, because it will be cut off there. The image is about 10% larger than the physical screen will show. To us, it means we can't show a full 640 pixel image width. We can only see about 90% of that width, which you may want to take into account for photos. 90% of 640 is 576 pixels. Overscan varies with TV sets, it won't be exact, you may want to experiment. To see all of the image, my own preference is to keep the image within 576x480 pixels (just my opinion). This is 6:5 aspect ratio.
If you want to show your entire uncropped image, then make it 576 pixels wide, and let the height float smaller, like 576x383 for 3:2 images - it will view with a black border at top and bottom. Or make tall images be full 480 pixels height, and let the width float smaller, like 319x480 pixels for 3:2 images, with the black border at the sides. Irfanview batch and Photoshop menu File - Automate - Fit Image offer this automated resampling decision regardless of image orientation. However the image can view considerably larger if you can crop the excessive long ends first.
If you want images to fill the full screen (without any black edges), you must crop landscapes to the 4:3 or 6:5 shape (see how here, but this cropping for full screen is optional). Then resample them to 480 pixels height (bicubic) but don't allow more than the maximum width. The image dimensions should fit within the full 640x480 or the reduced 576x480 size you choose (if NTSC, or for PAL, the full 768x576 or a reduced 691x576 pixels).
After resampling, then sharpen modestly (USM 0.8 Radius for video), and save as JPG Quality 9 (High Quality). Save this as a copy, don't ever overwrite your larger archived master file.
Many people use fancy video software like Adobe Premiere to create "movie" DVDs, with sound and motion. The television screens are still the same size, but the trend today is to use large still images, a few megapixels, to allow zooming and panning in Ken Burns style. The software will resample to output the correct size smaller screen image for each frame. That subject is "video", not scanning, and I can't help with that. Read your manuals, and maybe see www.videohelp.com.