The Fireworks .png format is an enhanced version of the standard .png format, to allow it to handle the vector shapes and other special data that Fireworks uses. If you save a .png from Fireworks, you get a Fireworks .png.
When you want to create an image for use on the Web, you want to have a .gif, a .jpg, or a flattened .png (a standard, flattened bitmap one, not one of the enhanced FW ones with lots of extra data). These are the "suitable format" options. To do that, you want to export from FW. You can either use File>Export... or File>Image preview... to set up the parameters for the export. (You can set some parameters when you create a slice, too.) Personally, I like the Image preview... option.
Create a new FW image, maybe with a couple of rectangles on it, and experiment with the options under File>Export... and File>Image preview... to see what's there and what you prefer.
Excuse the lateness of my reply but thank you! That pretty much answered it!
Yeah, nothing like being clear...
As always, it's .jpg for photos and .gif or .png for line art. Oh, yes... Firework's PNG 32 is the same as Photoshop's PNG24 with transparency; FW's PNG24 does not have transparency; FW's PNG8 is an indexed 256-color palette (like GIF), except that it does support multiple semi-transparent values. See:
The PNG8 format is very useful when you have a piece of line art with limited colors, where you want transparency, and you don't want to code for PNG32 functionality.
If you do export to PNG8 or GIF, you might find that you don't get all the colors in your image. It's been this way for a long time. You can use Image Preview and manually add values to the palette with the eyedropper.