I'd try to check each individual component before I 'shotgunned' the problem, replaced things that might not be broken, and spent more than needed. The relay in your '99 is solid state. It switches on and off very quickly to control the fan rpms. If you have a VOM, you could unplug the fan, and check for an open circuit, which would definately indicate the fan has taken a crap. You might be able to check your coolant temp switch the same way, although I think the impedence varies with temperature. But once again, an 'open' means defective.
All that's to the best of my aging recollection.