Most birders see warblers during the spring and fall; a short period in spring, and a bit longer in fall. They are often high in trees and difficult to get a good look at. Every season you'll get a warbler or two that comes particularly close, sometimes in low shrubs, sometimes on the ground. Even if it is one of the common warblers it's a spectacular experience. I personally look forward to those moments, especially in the spring.
One of the first birds I ever held was a Brown Creeper. These birds are hard to spot in the woods as they spiral up the trunks of trees. They are as flat as the bark and they blend in perfectly in cryptic streaks of brown. I am often cued into their presence by their very high pitched and almost inaudible calls. Once in the hand they seem even smaller than they did from afar on the trunk of a tree. Just like woodpeckers these birds have stiff tail feathers which they use as support when climbing trees. When one pries its long curved bill under a piece of bark its tail acts as a third leg to lean back upon.
In the hand the Brown Creeper is like a minuscule work of art. The details in the plumage are spectacular and the tail is so stiff it feels like hard plastic. However, they are so small they fit perfectly into the center of your palm, able to be fully enclosed by your fingers and thus barely visible.
Bird banding is an amazing way to introduce people to the world of birds, birding, and bird conservation. It gives a sometimes once in a lifetime view into the lives of birds, by seeing adaptations up close. It shows how unique an individual can be: one cardinal bites, and another does not. But it is only an introduction into a vast world. To witness natural behavior you have to take to the woods, fields, lakes, and mountains. Backyards also work fine for a starting point.