I use AWS for everything. As has been said, a static site can be served through S3 no problem. If you want https you can route through cloudfront. Domain can be pointed right at the bucket, I do that regularly for clients on a budget (practically free).
I do all of this VERY regularly, hit me up if you need anything at all.
As for whether S3 would limit you in future, it really depends on the type of dynamic content. You can host html, css, js, and images on S3. Anything static. If your js pulls from, say, the YouTube api, that is fine - the dynamic bit is handled on their server based on your request.
Once you start using PHP, Java, or another backend language, then you'd want to move to an EC2 instance (typically). You COULD use Lambda or another such tool (also on AWS) to do software as a service while keeping the page that serves content on S3, but you're starting to really split up your application at this point. Not a BAD thing per se, but perhaps a tad difficult to manage if you're not used to a component style of work.
If you let me know what you're looking to do I'm sure I could easily let you know specifics on tools and costs.
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Edited: 03/08/2019
at 03:54 PM
by Gloves