Rent or borrow a lens. It is the best way to get a feel for what you gain or lose depending on focal length and quality. Most good bird photographers are shooting birds in flight with 400mm or longer and 600mm to isolate in the field. 300mm with a 1.4x multiplier can work too but you lose some clarity.
I think of it this way.. The camera and its megapixels are what many people focus on but it is usually the lens that is more important. If you invest in a high quality lens, you will find you will be buying new cameras but keeping the same lens. It is a much better long term investment. So aiming for the best lens you can afford is the smart thing to do.
300mm on a song bird 40 foot up a tree will not do much for you. Half the trick in bird photography is not to have the bird 40 foot up a tree

One trick i use is to find a cliff or overlook roughly level with the tree tops in a known habitat for the bird i am interested in. Now your 300mm might work for you. There are plenty of other tricks if you read around and talk to other photographers that help you when you have a shorter lens.