Re-sizing an image making it smaller issue

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I need to clean up my forum logo for my forum. I can?t seem to get it very clean or sharp image when I resize it to a smaller size. I have tried everything I can think of in photoshop to make it smaller without losing clarity.

This is what I have discovered.

When resizing it in photoshop and making it smaller it gets very fuzzy. I am going from the pixel size of 1500 x 247 down to 500 x 82.
However if I keep the larger image of 1500 x 247 and resize it using html code like this width="500" height="82" the image looks a little cleaner.

Here are my questions:

1. Does anyone have any suggestions about downsizing an image and keeping the sharpness and clarity in the image?
2. How would I add the following html command to my title image so that I can use the larger image width="500" height="82"?

Here is the image I am referring to.
The original image:

Resized smaller with photoshop: