Is Budokan a good and reputable branch of Karate?

It sounds like you answered your own question. If Budokan is recognized by the World Union of Karate Do Organizations and the World Karate Federation, then clearly it has some reputable standing in the martial arts profession. If you keep digging you will probably find out that it has even more accreditations. I know it's a good art if it's featured in 'The Journal of Asian Martial Arts'. If you dig through their archives you should be able to find an article or two on Budokan.