My assumption about basic income was always that at it's core, it provides the money for food and shelter. This reduces bureaucratic overhead in terms of trying to provide people those goods, and gives them the freedom to make their own choices and not have to work to survive, and the government is no longer forced to create the infrastructure to try to find ways to provide food and shelter. This may, however, require work in terms of providing affordable housing options to everyone, but I don't think you have to solve one problem first to solve the other.

Health Care and Education are a separate (but still related and important) set of problems. Both of those require greater infrastructure on the part of the government to provide effective solutions, so again this is a problem that also requires a lot of thought and effort, but providing basic income doesn't seem like it would preclude health care/education reform. Nor does it seem like solving health care and education reform would change the structure or overall effects of a basic income program; they're simply additional solutions that would certainly improve our quality of life and possibly the efficacy of the program.