Firstly, I don't really recommend a remote job as a start in your career. There's so much you can learn from physical interaction that will be valuable later on in your remote job. So if possible, try to get out first from your city and spend 1 or 2 years in physical office. Having said that, we did hire a junior developer in the past. We met her at a conference and were impress with her presentation. So we approached her and asked if she's interested to join us. She still at uni at that time so she joined us as an intern first.
So you can make yourself stand out from the crowd by focussing on certain skill set (she's in UX and her presentation also about UX). Demonstrate your understanding in that area. The major concern when hiring remotely is whether that person is dependable. Dependable doesn't mean you have to be online 24/7 but you have a predictable behavior. For example when we need something from you, we know for sure you will come back to us in certain amount of time. Lot of people seem to fail at this, especially if this is their first remote job, even though they're quite successful in previous job.
You can read more about communication in remote work in our blog - blog.xoxzo.com/2016/04/22/the-comm....
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