GDPR is indeed very much the current "gold standard" of data protection laws, but it's just the latest in a line stemming from EC Convention 108 back in 1981. Just complying with GDPR will get you a long way, but some other (non-EU) jurisdictions might have laws that are specific to them, so you will need to do some research if it's applicable. The text of the GDPR itself is quite readable, but I find this unofficial reformatting of GDPR more useful - better searching, easier navigation, more cross-referencing.
The process of figuring out what you might need to think about and do is also defined under GDPR - it's called a Data Protection Impact Assessment (DPIA) (has much in common with higher-level Privacy Impact Assessments, PIAs), and you might find this tool by the French data protection commissioner (CNIL) useful; it provides a guided path through relevant concerns and helps you find and answer the questions it poses, resulting in a nice report and action list.
You need to be able to answer questions like these:
- What data are you collecting?
- Does it include "personal data" in the GDPR sense?
- Why are you collecting it?
- What right do you have to the data (i.e. what is your basis for processing?)
- Where are you keeping it?
- Who has access to it?
- Is the data shared with any third parties? If so, on what terms?
- How long are you going to keep it for?
- How are data subjects (the people the data is about) informed that you have the data and how can they request to see it, amend it, or request its deletion?
- What steps are you taking to protect the data (e.g. TLS, encryption at rest, password hashing)?
If all this sounds difficult, then you're getting the point of GDPR - being able to use people's data is a privilege that should not be taken lightly, and if you do it, you're going to need to step up. There is an easy way out - don't collect personal data; data that is not connected to a person is not personal data, and is exempt from GDPR; think weather info, stock prices, etc. Note that "personally identifiable information" (PII) is not a term or concept that exists in GDPR; that's a US invention. A colour is not personal data; a person's favourite colour is.
It may be possible to collect detailed data so long as it is anonymised (any link to a person is removed or rendered useless), though that is surprisingly difficult to do effectively.