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It would be nice to know what size droplet you currently are working with. I’m going to guess a 512 MB droplet based on the challenges you’re encountering. My experience with a LAMP stack is that 1 GB helps you get by with the common background services (httpd and MariaDB/MySQL) involved.
Wordpress’s RAM requirements is deeply dependent on the plug-ins you will have running on your site. Bare metal you can get away with 512 MB but with more plug-ins 1 GB is preferred.
I think with Joomla you can use it bare metal with 512 MB of RAM. More plug-ins and extensions will likely require more RAM.
One thing you didn’t cover was expected volume these two apps will create on your server. Higher expected volumes will require more compute resources (CPU and RAM).
If you’re running database-driven websites, I’d start with 1GB of RAM – even if traffic is minimal. That should give you a little breathing room to work on your projects without any issues.
While you can run LAMP and LEMP Stacks on 512MB of RAM, you need to know how to tweak and tune the configurations to work in such a low-resource environment. Apache and MySQL can take up quite a bit of RAM on their own, which makes 512MB dwindle down to nearly nothing relatively quick.