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Go for a $5 512 or a $10 1GB droplet, install Nginx (there are plenty of guides on DO community guide section, and then use Cloudflare free plan to CDN/Secure/Optimize your site.
You can easily do it with a $5 droplet and no need to host images else where.
When a client requests a page from a server, the server closes the communication with the client after doing his work. Sooo static pages requests do not need loooooot of RAM.
I think 2GB is also more than you really need. If you can, anyway, maybe it’s better to store images on services like Imgur, to save some memory…