The biggest health problem you will face raising goats is control of parasites, especially stomach worms. Some goats (Kikos in particular) have been selected and bred to be parasite resistant, but that does not mean parasite free. Parasites can debilitate and even kill a goat quickly. Regular worming is used by most goat farmers (perhaps in the spring and the fall). Additional worming of any particular goat is best done on an "as needed’ basis. The overuse of worming medications can promote the development of resistant parasites on your farm - a severe management situation you definitely want to avoid!
You can test for the presence of parasites by doing fecal smears and examining the feces for the presence of worm eggs under a microscope. This test can indicate the relative quantity and type of parasites present (worm load). Another easy test you can do on your own is the FAMACHA test that requires looking at the membranes under the eyelids of goats. The degree of anemia is estimated by observing the degree of redness in the membranes. A website describing this test and the color scale is: http://www.new-agri.co.uk/03-2/develop/dev04.html. Please remember, no "test" is foolproof. Careful judgment is also required. Seeking professional training in workshops for performing the above tests is strongly recommended.
A primary preventive measure against worms (other than genetic selection) is rotating pastures so goats are always eating in a significantly worm-free environment. A rotational strategy may range from daily to 3-4 week intervals depending upon the size of the paddocks. Browsed paddocks should stand dormant for 12 days to 6 weeks or more before the goats are rotated through again. Appropriate dormancy periods depend upon the size of the paddocks and the frequency of rotation. Your county extension agent may be a good source of information regarding rotational grazing strategies for your area.
Worming medication can be given orally or by injection. Most breeders periodically rotate wormers to decrease the chances of developing resistant strains of parasites. Talk to, or access information, from other successful breeders regarding the various types of wormers used and the appropriate dosages. Not many worming medications are formally approved for use in goats, so several "off label" uses have been developed. Your local vet may also be helpful regarding parasite control. Be sure, however, to ask about his or her level of experience with goats. Many vets have not worked much with goats, but this is slowly changing as the interest in goat farming increases.
Other parasite problems are skin related. Some conditions to look out for in your herd are lice, mange mites, and ringworm.