Last year, I sat down with the director of Stanford's Neurosciences PhD program, Anthony (Tony) Ricci, and asked him what he looked for in grad school applicants. Tony thinks a lot about what are the markers for success in graduate school, and in science. Your question is a great excuse for me to repost our discussion, which you can read at this link.
The biggest piece of advice: get experience working in a neuroscience lab. After you graduate from college, seriously consider getting a job as a research assistant in a neuroscience lab (see follow-up below). The greatest asset you can have as a grad school applicant is a demonstrated ability to work as a independent researcher. Your letters of recommendation should describe how you took ownership of a project, and acted as more than a pair of hands to be directed.
As for skills/knowledge, math and engineering skills are highly valued in the neuroscience community. Knowing what to do with, say, big data, is a skill in very high demand.
Mollie, it sounds like you're on the right track. Best of luck!
Follow-up Question: Where do labs post research assistant jobs?
Most academic institutions have a dedicated job posting site. Labs looking to hire a research assistant will often (be required to) post the job listing on that site. For example: Stanford's Job Search website lists research assistant positions under the title of 'Life Science Research Assistant'. Alternatively, try Craigslist. Two of the lab's I've worked at have advertised and hired multiple research assistants via a Craigslist ad (in fact, that's how I got my own RA position).