not too savvy on monitors.
Here is what I have . What would be a good upgrade and maybe what could I expect to gain?
Your computer looks very good to me. However, as Chalenge already said, your current resolution is low compared to what your GPU is optimized for. So my recommendation is to get a better monitor.
There's three features in monitors that you have to find a balance with: Image quality, speed and size.
The first can be achieved by increasing the resolution. 4K has been mentioned, and 8K is on the way. However, having to draw four or sixteen times the amount of pixels compared to a 1080p monitor at least 60 times in a second is still too much for most video cards. Plus you wouldn't really see the difference on a small screen, 4K should be way above 30" to benefit from the better image.
Speed is another issue. Your GTX970 should be able to run any game at a solid 60 FPS on a 1080p monitor. Cutting some of the settings down a little should perform well even on a 144Hz monitor. Size doesn't matter until the screen is so big you see single pixels instead of an image.
Size has already been mentioned a couple of times. A large screen adds immersion, there's no arguing about that. I love my 30", but if I had the space on my desk I might want a larger one. A friend just got a 46" monitor and it looks awesome. For the same image quality a 4K screen should be 92" which could already be an issue with wife ack.
I can't tell you anything about brands and models, but either a 1080p@144Hz or a 1440p (2560x1440)@60 Hz should make you happy for a long time. For both the size should be at least 24", for the 1440p rather 30".