You can also prerender the tiles on a powerful machine and host them on a cheap instance (assuming you don't need very large regions). A while ago I created an OSM server (https://github.com/seemk/TileSweep) to do this for me, you can select regions you want to render via a polygon and you get a SQLite database of the tiles. It can also run as an alternative for mod_tile + renderd.
I rendered all of Estonia from zoom levels 0 to 18 (~16.5M tiles) which is around 20GB and host the tiles on a cheap DigitalOcean instance.
I rendered all of Estonia from zoom levels 0 to 18 (~16.5M tiles) which is around 20GB and host the tiles on a cheap DigitalOcean instance.