Image Size reduction and gain resolution... Help?

I have searched the forums and seen plenty of talk of Image Size and resolutions but havent stumbled upon what I need.
Hopefully someone will be nice enough to help me or to link me to help?
I have a large photo (3456x2304) but it is at 72ppi.
I am trying to use it as a very small image (200px or so) but I need it at 300ppi.
I keep going into Image Size and reducing its dimensions to the size I need and marking 300dpi.
Problem is when it resizes it gets horribly pixelated!!!
I cant figure out how to use the image size and/or crop tool in order to reduce the dimensions and not lose quality.
Best work around I have found is to reduce it to about 750px 72ppi and then in illustrator contract the image to the actual print size while gaining resolution...
Any help would be greatly appreciated.

There is a relationship between image size and ppi (resolution)  that can not be changed.  Here is an example from the web titled "understanding resolution".
Let's say you have an image that is 9 inches wide and 6 inches high with a resolution of 240 pixels/ per inch (8.9mb file).  If you change one of the values the other two will change (resample image turned off).  In this example if you changed the width to 6 inches the height would become 4 inches and the resolution would become 360 ppi.
So if you are taking a large image and reducing the size the ppi has to go up.  There are the same number of pixels in the picture, they are compressed into a smaller space.  The article says this is because a digital image has no absolute size or resolution.  All it has is a certain number of pixels in each dimension.
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