What to start reading (with samples) with my current level?

I feel like stuff from the absolute beginner book club might be what you are looking for?

You could have a look at their past books too. In particular
Book 3 | しろくまカフェ
Book 4 | チーズスイートホーム
Book 5 | 結婚しても愛して

I don’t know what counts as “‘cool’ to read through”, but those look reasonable. Plus, the club has a ton of vocabulary and grammar explanations to help you through those.