I suggest aws (probably elasticbeanstalk, maybe a raw box) simply because it's a very well trodden path. Lots of helpdocs, tutorials, instructions, etc etc etc.
Assuming you're a professional in the US / west europe, etc, the diff between $20 or $30/mo and $5 or $0 per month is negligible, while the time savings just from staying on a standard path can be huge.
My default suggestion would be:
Elastic Load Balancer, to talk to the internet and terminate SSL;
Elastic Beanstalk or something similar to host a box;
Certificate Manager for your SSL cert;
Route53 to serve your DNS.
All of the above should be cheap and, again, a very well trodden path with tons of help docs and people familiar with configuration.