if I save image 3.5x5 inches with 72ppi and then print it from my website, size is incorrect (about 2 5/8 by 3 3/4) If I save with 300ppi - it's huge and won't fit on one page when printing... How do I save one image that will look right (correct size) on both paper and screen ?
There's lots of questions on this site pertaining to image resolution. Reading through those will help.
The bottom line is that (until recently) screens are much lower resolution than printers are. Most screens are around 100 pixels per inch and most printers can do 300+ ppi.
As such, you typically need to make two versions of your images. A lower resolution for the web, and a higher resolution for print.
If you want to use just one image, then realize they will likely be different sizes. For instance, a 100 pixel image on a 100ppi screen would be 1" wide. On a 300ppi printer, it'd be 1/3" wide.
If you're not concerned about printed image quality, however, you could simply place your image on a web page, scaled to the HTML page itself, and let people print that. It will look pixelated when printed, but will get you closer to an 'actual size' output.