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.