A biochemistry major may be right for you. In it you will learn your way around a modern laboratory. People who are interested in being technicians or research assistants are hired because of what techniques they can do. Yet science and technology are moving so fast that it is clear that the things that you learn as a student you may not be doing 5 years later. So in addition to having learned techniques, you also will need to have a firm grounding in the theory so that you can learn new technologies and them make work.
Modern science is done by teams.
The stereotype of the lonely scientist is a myth. If you work well with others and if you are often the leader in group projects, then you may fit very well into a biochemical career. That depends on what you want to do. If you are interested in polymers or inorganic chemistry you may want to consider chemistry. If you want to specialize in education or the more macroscopic areas of biology, you should consider biology.