@etzbseder:
I think you should also list the best tests to have done, so if people can't do many, they can at least know which ones to do first.
The Canine Health Information Center (CHIC) has a list of recommended testing for many breeds. They are co-sponsored by AKC and OFA, and the parent clubs for each breed are who decide what tests are important for CHIC certification. Here is the page for Basenjis:
http://www.caninehealthinfo.org/brdreqs.html?breed=BJ
So basically the Basenji community is saying that you should focus on hips, eyes, thyroid, and fanconi (which recently replaced the hemolytic anemia test). Dogs that have those tests done and submitted to OFA/CERF will receive a CHIC ID, whether or not the test results were positive. Wouldn't that be something to some day see all breeders and pet owners getting their dogs "CHICed"!
Other tests I personally like to add to that list are elbows, patellas and cardiac screening. If you do elbows at the same time as hips, it's usually pretty reasonable. Patellas are easily done during your yearly vet exam for nothing extra other than the OFA report fee. Same with a cardiac exam, although I prefer to use the clinics at shows where there's a cardiologist for extra thoroughness, and minimal cost.