Can I make sure customers get only the bigger discount, not the sale price plus the coupon?

Yes. Set the coupon's Discount application strategy to Compare-at price. If an item is already 30% off and the coupon gives 20%, the coupon adds nothing. If the coupon gives 40%, the customer gets 40% in total, not 70%.

Learn more: How to apply discounts to products already on sale? · Combining different discount types