Corrections to your statements or quotations
Your quotation "To fall within the remit of the GDPR, the processing has to be part of an "enterprise" (...)" is not from the GDPR, and is an erroneous statement.
Also, the threshold of 250 employees you refer to, is only relevant with regards to the record-keeping obligations of Article 30.
GDPR provisions relevant to your question
The GDPR applies to individuals or students in accordance with the material scope of the GDPR, which is treated in Article 2 (2) c) where GDPR states that "This Regulation does not apply to the processing of personal data: (...) by a natural person in the course of a purely personal or household activity;"
The Recital 18 of the GDPR gives some insight as to what would be a purely personal or household activity as follows:
(18) This Regulation does not apply to the processing of personal data
by a natural person in the course of a purely personal or household
activity and thus with no connection to a professional or commercial
activity. Personal or household activities could include
correspondence and the holding of addresses, or social networking and
online activity undertaken within the context of such activities.
However, this Regulation applies to controllers or processors which
provide the means for processing personal data for such personal or
household activities.
Interpretation
To my knowledge, there are no specific guidelines regarding this matter to date from WP29. Those may be adopted in the future, or some requirements may already exist in local laws in one of the EU countries or from documentation available from local data protection authorities. If you are based in the EU, you could check this with your local data protection authority.
There is, however, case law from the European Court of Justice as pointed out by Free Radical, interpreting the scope of the "personal use exception" in Directive 95/46/EC (which provisions are similar to the GDPR in this matter).
If your hobby is not limited to your personal circle (yourself and the persons in your household), and thus if you plan to share the results of your data collection and processing with third parties (possibly teachers, other fellow students, or anybody else if you publish the results of your work) resulting from your "hobby" activity, you certainly would not fall in this exception to the scope. Case C-101/01 is an example of publication on the Internet made by an individual claiming to use its "freedom of expression to create internet pages in the course of a non-profit-making or leisure activity". The court clarified that:
exception must (...) be interpreted as relating only to activities
which are carried out in the course of private or family life of
individuals, which is clearly not the case with the processing of
personal data consisting in publication on the internet so that those
data are made accessible to an indefinite number of people
Another, less optimistic interpretation from the examples given by the GDPR recitals, could derive from the spirit in which purely personal or household activity are to be understood. These examples actually refer to limited amounts of data and which are related to the individual itself (his own address book, his social networking activity, etc.), and creating limited risks relevant to the person herself and its contacts. In this view, there is a risk that a "hobby" in which you collect data about thousands of persons unrelated to you, could be considered as not being really purely personal.
Actually, an interpretation of case law C-212/13 from the European Court of Justice also mentioned by Free Radical could support this reasoning.
In this case, a video recording of people was stored from cameras installed by an individual on his family home for its own security purposes, but the cameras were also monitoring a public space. The court ruled that:
To the extent that video surveillance such as that at issue in the
main proceedings covers, even partially, a public space and is
accordingly directed outwards from the private setting of the person
processing the data in that manner, it cannot be regarded as an
activity which is a purely ‘personal or household’ activity (...)
Extending this reasoning to your question, a "hobby" consisting of collecting "huge list of names, emails, zipcodes" unrelated to you could be regarded as "directed outwards from the private setting (...)".
Conclusion
As a hobbyist, or a student, if you can work on fake computer generated data and achieve the same results in your personal learning purposes you should definitely consider doing so.
