Your gear will not hurt or stunt your progression. Yes you will fall when learning (and some people become discouraged), but it's not the gear. If you train on less-than-ideal gear, this will make you a strong rider. When you know what kind of board you like or what kind of riding you want to do, you will enjoy your next board so much more and feel an instant boost in riding joy. But if you are a beginner now who is just learning how to ride, you will not reap the benefits of better gear, there is no instant boost of ability or joy.
If you really train and challenge yourself in improving riding technique, you can buy new gear near the end of the season (Feb) for like 50% off. There will still be good conditions on the slopes for you to rip on your fresh gear.
Part of the fun about snowboarding is the learning curve, challenge, and progression. If I give you magic powers that instantly allow you to spin 360s or whatever, you miss out the fun.
Your 160cm is the right size. If your boots and bindings are uncomfortable, then you should get something better. Also you need to stay warm and comfortable with the right clothing.