Anton, follow the advise of the replies and get the elementary books. I’m not sure how kids in Taiwan learn these days, my mom says she see kids writing the characters wrong all the time, even among high school level, so I’m pretty sure the level has gone down.
When I attended elementary schools back in late 70s, 50% of our homeworks were writing basic Chinese characters, we’d write those repeatedly (at least 40 times for each word), we’d spend 2-3 hours a day outside schools doing this for 6 years, yup, from grade 1 to 6. Purpose was to perfect your writing skills, not just been able to write. 6 years of those gruelling work covered only the basic characters (I think less than 6000)
2 tips to get your skills quickers.
-Word root, get a dictionary, each word has a root, ie: fish, water, human, hand, heart, etc. In a dictionary, they go by number of strokes.
-Still have trouble finding a word? Use NJ Star, just put the pinyin and the word options pop out.
But I’d get the elementary books though, I think grade 1 to 4 will cover enough to write basic composition, again, it’s a lot of work, but can be fun though through how words are put together with a root.