I have done the AWS path in the past (and I'm pretty good with AWS mind you). In hindsight I would absolutely go with a $5 DigitalOcean droplet in the beginning. Focus on the product.
+1 to the DO droplet. You can start with one of their pre-built images in no time and don't have to deal with things you don't care about for this project like IAM, VPC, regions, etc. You can run Redis and your db locally on the box for a small app.
I used a aws t2.micro 3 year reserve for a side project. It works out to about $5 a month. I also had a few different services, I just put them all on one machine.
I've been looking at DO and something that strikes me is the 20% backup fee, with ebs, the thought backups never even occurred to me. Maybe they should've.