The material scope of the GDPR (Article 2) is limited to the processing of personal data (including mere storage) by automated means or as part of a filing system.
The question of whether your activity falls within this scope hinges on what you actually do with the data once you take possession of it. You have mentioned saving the contact information of people you have met at conferences, which could refer to simply retaining it for later use, or to the technological process of storing data in a computer. The former, if not done in any structured way (a filing system) would not fall within the scope of the GDPR. The latter, even if poorly executed, such as a photo stored on a business smartphone or a text document thrown onto your workstation's desktop, would always fall within scope as computerised data is processed "by automated means".
When the contact information you receive identifies a specific person, as distinct from just a corporate switchboard number and company name for example, it is personal data. When you get that personal data from the person it identifies (data subject), and you're otherwise in scope, Article 13 is invoked, requiring you to provide a list of information, "at the time when personal data are obtained", unless "the data subject already has the information." This is known as the right to be informed. The requirements differ when personal data are not obtained directly from the data subject.
You will of course be required to comply with other requirements such as the principles of data minimisation and identify a lawful basis, maintain adequate security by implementing technical and organisational measures, hold contracts with any third parties who process personal data on your behalf, and have a process for upholding data subject rights and responding to requests to exercise them - among others - but you should already be doing that for your other processing activities unless exempt.
Edits have been made as clarifications and questions were forthcoming.
You need to consider the applicable country's implementation of Directive 2002/58/EC as amended ("ePrivacy Directive"). For example, in the UK you could send such messages without consent to contacts at incorporated companies or public sector bodies, but would have required consent for sole traders, private individuals, or partners in an unincorporated partnership. In Ireland, you have an exemption to consent for existing customers who were offered the opportunity to opt out when their email address was collected, but must use the email address for marketing within 12 months. Each EU country will have a different implementation of the Directive. In the Netherlands, Article 17 of the Telecommunications Act implements Directive 2003/58/EC and thus provisions for direct marketing by email.
Processing by automated means
Processing by automated means refers to processing of personal data in electronic, rather than manual form. All electronic processing is within the material scope of the GDPR, while only manual processing that forms or is intended to form part of a filing system is.
The protection of natural persons should apply to the processing of personal data by automated means, as well as to manual processing, if the personal data are contained or are intended to be contained in a filing system.
‘processing’ means any operation or set of operations which is performed on personal data or on sets of personal data, whether or not by automated means
ICO guidance What is personal data?:
The GDPR covers the processing of personal data in two ways:
- personal data processed wholly or partly by automated means (that is, information in electronic form); and
- personal data processed in a non-automated manner which forms part of, or is intended to form part of, a ‘filing system’ (that is, manual information in a filing system).