I'm a native Chinese but I don't teach Chinese, I think I can try to answer your question :) 1) 你想想再买吧 means "You should REthink (thoroughly) to buy it or not", which means the speaker may not recommend you to buy it. 你想想就买吧 is also grammarly correct but it means "You should think again and buy it". In this situation the speaker wants you to buy it. This sentence can be rude because it sounds like an order, which may be the reason why your Chinese book wrote that it is wrong. 2) 他的病还没有好,病好了以后才来上课。 (This is a correct sentence/statement) means "He's not well, he will go back to class when he's better." 他的病还没有好,（让他）病好了以后再上课吧。This sentence is also correct but it is a suggestion, which can be translated into "He's not well yet, (let him) go back to class when he feels better." 病好了以后就让他来上课吧。This is a correct sentence, using 就, it means "Let him go back to class when he feels well.", which, again, is an order. This sentence is often said by a teacher. 3) In summary, 再 means "re-", 就 can be used as an order, 才 is often used in a statement. We can discuss abt it if you have more new, different or more professional opinions. :)

你想想再买吧 sounds correct. It means "Think before you buy"(not recommended). Chinese has a lot of subtle things, especially for prepositions. 你想想才买吧 is quite wrong. 你想想就买吧 is not absolutely wrong. It can mean "Think before you buy" (recommended). The second sentence sounds ambiguous to me. 他的病还没有好,病好了以后才上课吧: Doesn't sound wrong. Say A is sick, B and C are A's friends. If B asks C, "Why is A still not coming to school today?", C can say "他的病还没有好,病好了以后才上课吧". It emphasizes that C is pretty sure that A can only go to school after he gets cured. 他的病还没有好,病好了以后再上课吧. Say A is sick, B is A's teacher, C is a doctor. If B asks C, "Can A come to school tomorrow? Exam is close." C can answer "他的病还没有好,病好了以后再上课吧". It is like giving a suggestion. 他的病还没有好,病好了以后就上课吧. Similar condition as 1, but this sentence emphasizes that C is just guessing. I am not a professional Chinese teacher but these are damn hard I don't know what's the best way to learn honestly.

就 and 再 have very different meaning. 就 indicates an action doing fast, period of time is short or one thing happens easily. “你想想再买吧” means the speaker suggests someone to reconsider his/her decision of buying something. So we cannot use 就 in this situation.

“再" indicates that what mentioned before"再" is important and should be done first. "他的病还没有好，病好了再上课吧"means only when he recovers, can he go to school. The recovery here is the condition. "就" refers to the thing happened very quickly after the previous one happened. For example, “他很饿，一回家就吃饭了” It means he was so hungry that as soon as he got home,he ate.

We can discuss abt it if you have more new, different or more professional opinions. :)