2. History. How long has the school been in existence? While new schools are formed all the time, having a longer tradition of offering courses, typically makes for better schools. Some of these schools have been open for decades as pre-Internet correspondence schools. This can be an advantage in producing quality programs.
3. Standard references. Is the school listed in one of the standard references like Complete Guide to Online High Schools: Distance Learning Options for Teens & Adults (Degree Press, 2007) or Bears' Guide to Earning High School Diplomas Nontraditionally (Ten Speed Press, 2003). Being listed is not necessarily a hallmark of legitimacy, but it helps.
4. Cost. Some of these online high schools are free public charter schools while others are quite expensive private high schools. The most expensive that I have come across is attached to a university in the south. Is there an advantage to paying more? Not really, but there may be an advantage with your program being attached to a university. However, being attached to a university most definitely does not mean that it must cost more.