G-Sync allows the Monitor to synchronise the Refresh rate to that of the graphics' card, making it look times smoother. In many games having G-Sync and an Nvidia graphics card will make them look butter smooth.
For you, someone with no experience with it it will make the games look times better. Now, you come from a quite old, not necessarily awful monitor. First of all, I would like to talk about them Hz. Going from 60 Hz to over 144Hz is a considerable improvement, and it will be very noticeable. You will be able to notice the difference by merely moving your cursor, the images will appear a lot smoother. Next, I want to talk about the Monitor panels. The monitor you're looking to purchase has a TN panel technology. TN panel is faster and cheaper than the ISP one, but it has poorer viewing angles and colours. I would highly recommend IPS for any use. IPS provides cleaner viewing angels as well as more vibrant colours and usually comes with higher refresh rates (Hz). Lastly, the size of the monitor. Now, I have been using a 27" Curved monitor for quite some time now (Approximately two years), and I can't see myself going back to a 24" one. Having a larger monitor will allow you to see details more precise and will make the overall image experience better.
Differences between Freesync and Gsync are scant. Both technologies do the same job, synchronise the monitor's refresh rate with the GPU one. The only significant difference is the fact that Freesync only works with AMD GPU (And selected Nvidia GPUs which can be found with a simple google search) and G-Sync is supported only by Nvidia's graphics cards.