Overall, unless you go to a private neruscience research firm or do private neuroscience research, persuing a career in nerscience academic might not be the most lucrative!
Medical school: To become a physician or surgeon specializing in neurological conditions, you can go to medical school and pick a specialization during your residency. This would require you to complete medical school applications, tests, and interviews. It is very expensive from what I'm told. But you will make a good salary as a practicing physician.
Graduate School: You can begin graduate school after you complete your undergraduate degree. Applications for grad school are not expensive, and the graduate programs pay for you to interview with them if you get selected. To boost your chances of getting into grad school, having research experience is crucial. I recently completed my PhD in neuroscience and I had a good amount of research experience during undergrad. While in graduate school, you get a stipend to live off of and your PhD education is covered (as in free) so you wont accrue more debt while in grad school. After graduating from grad school, you can either choose to stay in academia, i.e. become a post-doctoral fellow, principal investigator, staff scientist, teaching position, researcher, etc. or you can get a job outside of academia. There are many many options outside of academia - industry research, policy, consulting, NGOs. The pay would depend on your role and the company where you work. You can typically google certain positions and find out the median and average salary ranges for these careers to get a better idea.