Right. A few photos might help to identify which headset it is as you need one that fits your headtube. They come in several different types, so you need to know which one fits.
First, what happens when you take the fork out? Does the bottom bearing cartridge pop out easily, might need prying out if it's gungy? If it does, clean it up and look at the details etched on the outside. I suspect yours is an integrated Orbit type, for a straight head tube and 1 1/8" standard steerer. If this is the case it's the simplest one to work with. There are no actual headset cups, they should form part of the headtube, and the bearing simply presses into the cups machined or bonded within the headtube with your thumbs. Measure the width of the lower bearing recess (internal diameter) . The number of standards is confusing and you need to be absolutely certain before you go ordering. If it is the standard 44mm one it'll be an angular contact bearing, and this will form part of the details etched on the outer side of the bearing cartridge. The FSA Orbit integrated one should be 45degrees. You can order replacement bearings I believe, although given the prices it might be just as easy to order the entire headset, as this will come with new seal covers and a new crown race for your fork.
Does your headset have a brake cable guide on the top cover?
As for the crown race being rough, do you mean the crown race bearing, or the crown race attached to your fork? If that's rough or pitted you might be able to clean it up using fine wet'n'dry, or you may need to remove it (you can prise it off using a small slot headed screwdriver) and replace it with a new one. Again, a home workshop bodge is to use the plastic accessory pipe from a vacuum cleaner as a slide hammer to ram it in place.
A good value and excellent quality replacement for an integrated headset would be a Hope. They even have the advantage of a split crown race, which can be fitted and removed by hand rather than needing special tools or hoover pipes.