Hi Thenis, Caps are an easy change. The biggest difference will be made by changing any cap that is in the positive lead. These caps will be in the crossover circuit directly and not compensation circuitry. Any film cap should be an improvement over electrolytic. Grades in asending order are Mylar, polycarb, metalized polyprop, polyprop, poly styrene, paper & oil, teflon. Most companies today use Metalized poly propylene, the higher the voltage capability the better, these are generally a very nice improvement over electrolytics or mylar. It really depends wether the caps are series or parallel wired in the crossover to know how much difference the parts will make.
As mentioned earlier, switching coils or inductors is a little more tricky. Sometimes, a coil is wound in a smaller gauge to use its resistance in place of a resistor to cut the parts count in a crossover. If you can keep your resistance matched, it is typically much better (at least in tweeter & mid circuits)to replace iron ferite or steel core with air core, but resistance typically needs to be taken in consideration, it does depend on the coils use. I hope this all makes sense. To go much past this, I really suggest you buy a book on speaker building or find someone that has some real experience that you trust to guide you along the journey.
Good Luck,
Tim