In most neurology journal with decent impact factors, the turn around time if rejected outright is 1-2 days. If the paper goes through the review process and gets rejected turn around time is 4-5 weeks. If the paper makes it through multiple minor rejections and resubmissions to acceptance the turn around time to final acceptance may be 8-10 weeks. From submission to publication may hover around 16-24 weeks.
NB: It is highly recommended that one avoids dubious predatory journals that promise quick turn around times. Do a background before submitting to avoid predatory journals.
Turn around times can be highly variable even within the same journal. Providing a good list of reviewers to the journal is one of the best ways to accelerate this, as is providing a high quality product the first time around so that the number of resubmissions is limited. I've never seen a paper go through without at least 1 round of revisions, so expect to revise and do so quickly and thoroughly.
The way to have a high acceptance rate is to be realistic about the level of journal you are applying to. Have a nice case report? Don't submit to Annals or JAMA Neurology, you're basically buying a lottery ticket. Send it to Neurology Clinical Practice or the clinical subjournal for the subspecialty it fits in. Also don't send it to an online open access journal nobody's heard of - that can actually backfire and look like a CV black mark if it's a predatory journal that doesn't do proper peer review. There are good online open access journals out there (e.g PLoS, Frontiers, eLife), but it can be hard to know the difference without doing some homework.