Post processing is hugely subject to personal preference, but here's my opinion.
Don't over do the image, especially by jacking up the vibrance, contrast or sharpening, you want to enhance the image, not ruin it, especially with wildlife images.
I liked the big tree branches, so I've kept as much of it as I could to keep the whole image in context, but just adjusted the colour, contrast, and toning. The key to post processing is learning how to create layer masks and masking/unmasking parts of the image to enhance the whole picture. After I created a mask and adjusted the background, I was able to separate the birds with the background by changing the contrast, brightness and vibrance.
The thing you should learn first is how to layer mask and use it effectively.