I did some checking and the app requests about 130kb when it requests the registration list, and when it requests a check in record 2kb.
So 25 GB seems like it’d be enough if it’s only going to be used by the apps to connect to your site.
With regards to the server, we recommend upgrading to PHP 7 if that’s possible. The PHP version may or may not be available as a setting within your web hosting account.
Also, it may help to upgrade the server to a plan where more resources are available (depending on what’s currently available from your web host).
For example, Digital Ocean has a number of tiers available for their droplets: https://www.digitalocean.com/pricing/
If the current plan had a 2GB memory limit, an upgrade to a 4GB plan would be a nice upgrade. It’d also be an upgrade to go from a Standard Droplet to an Optimized Droplet.