I have a Nikon D90 which gives me several quality options (3) and image size options (3) for a total of 9 possible combinations. I have a printer which says that it has a resolution of 4800 X 1200 dpi.

So, if I want to take my pictures in the optimum jpeg format for printing on 4 X 6 photo paper (10 X 15 cm), which jpeg format do I set for my camera among the following options?:

Size options: Large (4,288 X 2,848), Medium (3,216 X 2,136) or Small (2,144 X 1,424)

Quality options: Fine (compression ratio 1:4), Normal (compression ration 1:8) or Basic (compression ratio 1:16)

I would like to understand all this but for starters just knowing what settings to make on the camera will suffice. Memory card size is not an issue at this point.

I take everything big as poss then crop and resize after.
A resized 4x6 should be fine and you still have a big file if you get a great shot you want to get printed bigger.

Shoot the BEST quality and largest size available! You can always resize any file to fit your 4"x6" paper after the fact, but going the other way makes for a poor image.

See my reply in the "Digital vs Film -- DL Warning:big File" thread about RAW.

Don't get digital file DPIs mixed up with printer DPIs. They aren't the same.

It takes a much higher DPI printer to do a good job printing a much lower DPI digital photo. Essentially, the DPI on a digital photo file is meaningless. If you only change the DPI on a photo file, the inch x inch "size" of the photo file changes. If you only change the inch x inch size on a photo file the DPI of the photo file changes. If you change both simultaneously on a digital file then yes you loose something. If you change both DPI and inch x inch size the pixel x pixel size will change. If you change the pixel x pixel size, either the DPI or inch x inch size will change. That is how these attributes are related in a digital photo file.

Displaying the photo on a video screen versus actually printing it out have different considerations. Suffice it to say if you are certain the photo will only be viewed on a video screen at a certain pixel x pixel size then absolutely take the photo at as close to that size as possible. Then resize down if necessary.

When you're planning on printing out the photo, the highest pixel count and lowest compression is usually the best bet every time. In what you are describing, the largest size and lowest compression is almost positively the best option.

Be careful resizing photos for print out. You typically do not have to change pixel x pixel size to get smaller prints. Always error on the may need to resize down side. Resize algorithms remove detail but don't add it very well.

Hope that's helpful.