As an MD student who just matched into neurology last week, I'm happy to add my 2¢
In general, big-name programs want to see applicants who are well-rounded with a successful track record through medical school, but also with the ability to "sell" themselves for why they will be a good hire for a program.
Given that the better-known programs tend to be academic, that means having a track record of doing research, publishing, and having an interest in pursuing an academic career tends to go over favorably, particularly if you can develop a skill or a niche that you can use to your advantage during the application process. That doesn't mean you have to be fully committed to one niche area as a medical student, but it gives programs more of a sense of who you might become one day and suggests that you're a go-getter carving out an area for yourself. The added benefit of finding a *good* research mentor is having someone in your corner helping guide you to residency.
That said, top programs expect a high level of competency clinically, as evidenced by your clinical grades, your letters of recommendation, and the board exams. You do have to perform well above average on your step exams for the well-regarded programs, particularly if you're not an MD/PhD. Just be aware that SDN tends to be overly exam obsessed. Scores get your foot in the door, they don't get you the job. Furthermore, for neurology (and for all residency programs actually) they do have a point where program directors don't really care if you scored higher. I got >260 on Step 1 and >270 on Step 2CK and I am very skeptical that my scores actually translated into me getting more interview invites than if I had scores in the 250s.
Clinical grades and LORs probably actually matter more than exam scores. If your school has them, AOA and Gold Humanism help. Having a good reputation in your school's neurology department (and internal medicine department, where you will also get a LOR) matters a lot, much more than people on SDN often discuss. It really helps to have your reputation as a good student precede you when you go on your IM and Neurology Sub-internships and before you ask for LORs. Especially since cross-institution phone calls occur to see if an applicant that looks good on paper is actually the real deal.
When it comes to applying, it's worth applying broadly without restricting yourself to a particular part of the country. Programs tend to be ~10 per class; not as small as some surgical specialties, but small classes mean that a particular place is less likely to be a shoe-in. Oftentimes big-name programs are predisposed to rank particular students coming from particular medical schools. Case in point, WashU nearly always sends 1-2 MSTPs to MGH/Partners. It's not that these spots are allocated per se, but it means there are probably fewer truly "open" spots going around than you might hope. Lastly, there is always a degree of randomness to the process. Best of luck! Feel free to reply or message me if you have more questions.