To offer a slightly more specific answer:
Right now, you're using the G20 driver, which is part of a set of clubs that have a high loft. Since the rest of your clubs (irons - putter) are all beginner/starter clubs, you're not going to be able to get much loft or stopping power, even with an upgraded ball.
It's both loft and spin that can affect that ability to stop the ball on the green. (The distance the green is above or below your feet along with winds also effect this, but that's another discussion.)
When looking at upgrades for your clubs, look at the trajectory and spin of the club. High loft combined with more spin dots mean clubs that are going to stop better when they hit the greens. If you can afford them, I would definitely recommend the G20 irons for both increased loft and spin, but also for the distance you'll want once you hit Master.
Another addition would be different balls. Even with better clubs, it's not likely there will be a noticeable difference. The combination of the G20s and the Calloway i(s) balls is an excellent pairing, with Calloways, in my experience, are the best for the price.
One more consideration would be to carry 3 wedges instead of the 2 and the hybrid. With an overall better combination of driver and irons, you'll find that you really don't use the hybrid much, if at all. A good span of wedges will help get the ball closer with better stopping than your longer irons. The Z Satins are a good deal with some good stats as well.
Good luck!