When I feel I need a break, and then continue again? Or does this make it more ineffective in terms of getting my heart/blood pumping + burning calories + gaining muscle?
For increasing cardiac fitness, i.e. strengthening the heart,
you can actually do “intervals” or repetititions, where you push yourself to say 85% of your max effort for say 3 minutes,
ease up and regain your breath for say 1 minute and then repeat, warm up at a steady rate for say 10 minutes first and do as many reps as you can comfortably manage, then warm down. If you are doing it to lose, or control weight or to add muscle, then steady state riding, where you are just out of breath, but can still talk, is the way to do it, stopping just means that while you are still you are not burning calories.
By riding at a steady rate regularly for as long as is comfortable, you will gradually improve your overall fitness and build muscle, keep a record of your time on the bike, and how far you travel, for day to day comparison, you can then see the gradual improvement.