Need of keeping data beyond each specific project

No, you need to know what data you will keep (maybe personal details in suppliers/customers invoices), how long you will keep them (usually bookkeeping periods are defined by law) and how you will protect and then you need to develop your own privacy notice to inform in a transparent manner how you will process personal data. If you do not keep projects data, you will write so to inform individuals about it. You need also to protect data with some security measures. 

Here you can find some information:

• GDPR challenges for small companies: https://advisera.com/articles/gdpr-for-small-businesses-the-most-common-challenges/
• Everything you need to know about the GDPR Privacy Notice: https://advisera.com/articles/gdpr-privacy-notice-6-key-elements-to-include/
• First steps to take to reach GDPR compliance: https://advisera.com/eugdpracademy/blog/2018/10/08/first-steps-to-take-to-reach-gdpr-compliance/

You may also consider enrolling in this online EU GDPR Foundations Course: EU GDPR Foundations Course: https://advisera.com/training/eu-gdpr-foundations-course//