latley I started using Nikon D3300.
Color space set to sRGB. My PC screen is simple Philips LED 24", also sRGB.
When importing NEF file to Photoshop, color space is "ProPhoto RGB".
My photos are for Web (PC, Smartphones..) and maybe some of them in the future for printing on canvas and photo paper (So I want to keep this possibility available)
I set my screen to "sRGB" color profile.
How should I import my NEF files? "ProPhoto RGB" or "sRGB 2.1"?
When importing, is "Camera Calibration" tab is related to the color space?
In the "View" tab, should I choose something in the Proof settings?
When saving my JPEG file, should I do "Save as" or "Export to web"?
You mention only having a simple Philips Monitor so I think ProPhoto might be more headaches than its worth as it would be nearly impossible for you to see what's really going on in your image.
Camera Calibration tab is not related to color space. Its for calibrating your camera and lens using something like an XRite Color Checker Passport
If and when you decide to print you could preview it but otherwise its not really necessary. Even when printing its not all that useful. If you need exact colors you need pantone and to trust the swatches. If you don't need exact colors than previewing doesn't matter as much as doing smaller test prints.
It doesn't make a difference. Save for Web just gives you more features for reducing the file size. If you're going to print though save as .TIF not .JPG