It depends on the layout of your site. Fixed width just means that the element will always be that size no matter the dimensions of the browser. So if you set a fixed width on say a banner or nav menu to 1024, then a person viewing the page width a browser width of 960 would need to scroll to the right/left to see the full banner.

Min-width and max-width just tell the browser that the element's width must be within a certain range. So if you set the min to 800 and the max to 1024 then the browser is allowed to resize the element to a size within that range if a visitor changes the dimensions of the website.

So it really depends on how you have your site laid out. If it's a typical non-full width type page, like this, then you should be fine with leaving the fixed width alone. But if you are creating a full-width page, like this, then you need to set the min and max width.