Preview isn't the best way to resize an image. Do you have PS, or Elements, or Lightroom? That's a better way to do it.
Resolution has no meaning for an image posted to the web. Pixel dimensions and JPEG compression that are the factors you need to consider. The best results for BPN are to post at the recommended max size of 1400 pixels horizontal by 900 vertical. If there is a lot of detail in the image you'll need to adjust the JPEG "quality" (compression) down. For viewing at that size, you can go down a lot before you see any difference.
You can use Preview to compare two images of different compression to see if there is any significant difference.