Amazon gift card top-ups and points
Amazon's top-up gift card (ギフトカード チャージタイプ) is basically storing money in your own account. It starts at ¥150, you can enter any amount, and the balance can go up to ¥300,000. You can pay by card, or in cash at a convenience store, an ATM, or through online banking, so you can still shop on Amazon without a credit card.
Cash top-ups used to earn a fixed percentage back in points, but that's gone now. Some accounts occasionally get offered bonus points on their first top-up, and there are often top-up point deals around big sales, so just open the gift card page and top up when you see a banner.
Your balance is good for 10 years, and checkout uses it first by default. You can't spend it on other gift cards or withdraw it, so it's safest to top up only as much as you'll use.
Points are worth ¥1 each, and you can use them by ticking the box on the checkout page. Regular points all expire if there's no activity for a year, counted from your last order or the last day you earned points. Limited-time points (期間限定ポイント) expire sooner, and you can find the exact dates on the Points (ポイント) page.