If you want to take this to a higher level, look at Constantin Vayenas, Der, die, das: The Secrets of German Gender (2017, 2019). The author, who had the same problem that all non-native German speakers have in deciphering gender classification in the language, sets about a serious study of linguistic patterns. He is Greek but knows Latin, which assists in unravelling some of the ancient mysteries.
Given that nouns constitute 70 per cent of the words in the German language this is certainly a very important topic for language acquisition. And particularly so when you have the worthy aspiration, as you do, to go on to serious writing in the language.
Yes, of course you can slur over a ‘d-apostrophe‘ or two, particularly in the spoken language, and you might try occasionally going ‘Southern German’’ (by turning words into the diminutive and giving them an umlaut and a ‘-lein‘, ‘-chen‘ or even a ‘-li‘ ending!) but you will be found out in the harsh spotlight of written German. And yes there are these baffling ‘wandering nouns’ too: Duden, the preeminent dictionary of the German language, points out that it was generally thought to be ‘das Virus’ as befits medical and scientific terminology with a Latin basis, but with the current pandemic and particularly in everyday language and increasingly on radio and TV it has become ‘der Virus’. So-called ‘multiple-gender nouns’ are just 1.3% of nouns listed in Duden, but it looks as though der Virus is rapidly following on the erratic trail of ‘der/das Laptop’…
Computers of course have assisted greatly in analysis and have highlighted some very interesting - and not always obvious - results. The author has two over-arching rules: categories and sounds. He points out that these classifications, and all their derivatives, are rarely ‘taught’. This is of course to the vexation of all German language aspirants, who are usually told, as Mark Twain was, to learn each noun’s gender ‘separately and by heart: there is no other way’.
But the author shows that there is assuredly ‘another way’, albeit not always simple, and he delves into a huge amount of detail, which is absolutely fascinating.
If you want to check even further into the statistical demolition of the traditional claim that ‘gender assignment is arbitrary and unpredictable in German‘ look at a Cambridge PhD thesis which proves it is ‘in fact a largely regular, systematic process’; Emma Corteen, The Assignment of Grammatical Gender in German 2018 www.repository.cam.uk
German children inevitably learn these ‘secret‘ pathways by immersion, but it is uncanny that when tested at age seven with ‘fake words’ they allocate gender in exactly the same way that adults do when taking these simulated linguistic tests; Dieter and Karin Krohn, Der, das, die - oder wie? (2008). At age five German children, when puzzling over some of the ’fake words’, tend to go for the feminine - not a bad guess as almost half of German nouns are feminine - but by age seven they become unerringly ‘accurate’! So there is most definitely a logic underlying the allocation of der, die and das.
I would thoroughly recommend the book by Constantin Vayenas as it has so many useful insights, backed up by percentages from the research. Occasionally I caught myself thinking ‘oh the author is just inventing yet another sub-rule to fit the random idiosyncracies of the German language’… but not too often! And his last three chapters, mercifully short, deal with some impenetrable remaining mysteries for the non-native speaker: ‘one or the other’; nouns with more than one gender; or even ‘nouns with no gender’…
There is even a list of five nouns using all three genders, varying on a regional or dialectical basis: der/die/das Bookmark, Dingsbums, Spam, Triangel and the infamous Joghurt (with very slippery spelling too, as it can also pop up on a shopping trip as Yogurt, Yogourt, Yoghourt…)