I would certainly recommend reading up on the GDPR legislation. There are plenty of summaries that are good and covers the important aspects. Because once you understand GDPR, complience can follow naturally while you develop your application. Even if you dont serve customers in EU, GDPR complience will benefit non EU residents as well, since you have then implemented tooling for proper management of private information.

And if your application doesn't store data, then it's a one time cost essentially. Which is the time spent reading up on the legislation.