Your photo file generally has a 'document profile', such as sRGB, aRGB (Adobe RGB), ProPhoto or similar.
The color management system insures that a correctly recognized document profile is rendered correctly on your calibrated monitor, using the monitor calibrated profile. If you print your document, you have to select the 'printer profile' associated with the printer, the paper and ink you are using. Your calibrated screen should take advantage of its profile to display the document profile as best as it can. The 'softproof' feature should simulate the rendering on your prints, knowing that not all colour shades you can see on your display can't be render as exactly (brightly, saturated...) as what you see onscreen.
To help you better and keep things relatively simple, we need to know the document profile, which depend on your camera or scanner.
Most devices use the sRGB colour space, which is not a wide one. However it's the most common one and if the document does not provide the information of the exact color space, most devices and softwares assume sRGB.
If you have a pro or prosumer camera, you can select sRGB or aRGB (a wider color space); you can also shoot raw, which is not a photo format, which has no color space, but which only records the intensity of light over each pixel.
You can also receive files with different profiles. A common situation is ProPhoto obtained by the raw conversion with Lightroom or Camera Raw (ACR). So, when editing, check the original profile embedded with the file. However, the wider the color space, the better colour range... or the worst rendering if the editing software thinks it's sRGB!
We also need to know your usual output devices: display, home printer, Web or local print service.
Absolutely avoid 1) No color Management.
Optimize for computer screen, means assuming sRGB ... if the profile is not known (embedded in the file)
Optimize for printing means assuming aRGB... if the profile is not known (embedded in the file)
Yes, it's important to understand that this choice is either for files without a known embedded profile or from a raw file, which has no profile, since it's raw...
If you shoot raw or if you have the ability to select aRGB on your camera, you can take advantage of the wider color space is you have a good home printer or if your printing service offers that choice.
If you set your choice to optimize for printing, the ACR raw converter will produce aRGB profiles. You can get better prints or even displays (with very good monitors). However, the same image will appear dull if displayed on most current displays which have no color management.
Elements can recognize many embedded profiles other than sRGB or aRGB (even ProPhoto) and work internally on those profiles. Your calibrated monitor will make the most to render them correctly. However, if you want to 'convert' to other profiles for specific printing needs, your only choices are sRGB or aRGB, which is a wise choice in my opinion.
Absolutely correct.
Note: for more learning about color management, have a look at the side from Andrew Rodney, the digital dog.