"은/는 and 이/가"
Which of them to use has nothing to do with whether the sentence ends with a verb or adjective.
Here's a simple introduction that might help.
The basic rule is that 은/는 is generally used to talk about important, open information as a main topic. 이/가 on the other hand is more for supplying a specific fact, in a closed manner, playing a subordinate role ("open" here means it has a nuance of wanting to talk more about it, while "closed" indicates it ends there).
은/는 is generally called a topic marker to distinguish it from 이/가 which is a strict subject marker.
- 나는 이 학교를 다녔다: I attended this school. It introduces new info about the main topic 나, so 는.
- 이것은 내가 다닌 학교다: This is the school I attended. 나(내) is in a sub-clause modifying 학교, so 가.
(이것 is the main topic the speaker wants to talk about, and 내가 is supplying a single fact in a subordinate role)
- 그가 왔을 때 나는 자고 있었다. When he arrived, I was sleeping.
(typical sub- and main clause arrangement: 이/가 in sub-clause, 은/는 in main)
AA: 누가 숙제를 다 했어요? Speaker wants to know a specific fact only, WHO finished the homework.
BB: 영수가 댜 했어요: Same. A single specific fact is given as an answer to a question asking for it.
AA: 철수는 아직 못했나요? Speaker draws attention to a new person, who becomes a new topic.
So, in subordinates phrases, it is typically 이/가: 내가 너를 좋아하는 이유, 내가 읽던 책, 정보가 중요한 시대, etc.
When one talks about something as a min topic, it is with 은/는: 나는 네가 좋아, 난 회사 그만 두기로 했어, 그 애는 죽었어.
Knowing these basic principles would be a good start for beginners.