...but the aspect ratio that is important.
For instance if your original image is 3.5 x 3.5 square, when you scan it should still be square. Not a 4x6 rectangle. This is to be avoided, as you are distorting the original aspect ratio and shape. I take it this is what you mean by "kind of distorted".
As far as being enlarged, this is the result of your scanner settings. Those scanning numbers you are selecting "300 - 1200" refer to the dots per inch that are being scanned. As each dot (a single pixel) is always the same size (1pixel x 1pixel), if you fit more and more dots in per inch, you effectively enlarge the scanned image.
For example : If you have a 1" x 1" postage stamp and you scan at 75dpi. The image is 75 pixels x 75 pixels. If you print out at 75dpi on your printer it's still 1" x 1" square. However, if you scanned at 150dpi, the scanned image is now 150x150 pixels (twice as wide, twice as tall) and if you printed that out at 75dpi, you'd end up with a 2x2" postage stamp. So to restore the printed stamp to it's original size you have to print out at 150dpi. This second option also leads to both a sharper scan and new print, as more pixels and dots are used to form the image.
If you are trying to easily print out an image exactly the same size as the original you have to consider the weakest part of the chain, and that's the printer. Often printer's highest quality maximum is 300dpi (check your own) so you should scan your images at that same setting. By doing so the image scanned will be the highest quality possible that your printer can reproduce at a 1 : 1 scale.
However, should you use some half decent graphics software, you can scan at 300, 600, 1200, (or whatever, but always avoid interpolated numbers) and use the software to control the size of the printed image.
By far and away this will produce scans that contain the most details (they will of course be very large file sizes, and be thousands of pixels wide/tall) and best quality reproduced images, but it takes work and time to size, and edit those pictures (you might soon be fixing errors, brightening colours, increasing contrast levels, adjusting gamma correction) which most users aren't interested in, nor skilled enough to do.
Now onto the final point. "Not clear". Again this is a result of the enlargment process, caused by high dpi scans. With each generation you lose quality too.
1st generation = image exposed to film
2nd generation = film printed
old age degeneration
3rd generation = image scanned
4th generation = image printed
As you are enlarging the image by scanning at high dpi settings, that small sharp picture (it's not sharp at all, but being so small you can't see that) becomes oddly less sharp. This is not an issue. The tiny details in the samll original image will look less clear if you use any powerful magnification to view. This is what you are doing with your high dpi scanner. You are magnifyiing all that less than perfectly sharp tiny detail, where it's now all very obvious. You can see this easily in any TV store where small portable TV's all look super sharp and bright, and even the highest end very expensive large screens TV's look nothing like as good. They are both displaying the same signal and picture, but all the details that look sharp on the small screen are shown to be far less so when they're all enlarged on the bigger screens!