Missing birds doesn't matter because they keep coming forever, and each missed bird adds one point to your overall score, while captured birds are worth more points. There are 12 kinds of birds, but they're all essentially the same except for their color and size, which determine the price you can sell them for. Selling is done in a separate menu where you can simply hold the mouse button and drag it over all the birds to sell them.
With the money, you can feed captured birds to increase their size and sell them for more. However, until you increase their value by upgrading their price with points, there's little reason to do so. There are also 108 bird variations based on color and size, and you have to upgrade the price of every single one individually. Each one can be upgraded up to 10 times, and every upgrade costs more points. It’s best to ignore this.
Besides food, your money is best spent on general upgrades, although they're not particularly exciting. To actually buy them, you also need to reach a points threshold, which starts at one million for the first available upgrade, the one-click kill, and then climbs into the stratosphere for the rest. So even if you have enough money, you still won't be able to buy an upgrade because points are also required as a form of currency.
As for the remaining upgrades, they include extra money from selling birds, automatic capture when birds reach the edge of the screen, and auto-sell. So yeah, there isn't much else. In fact, it's more of an idle game than an incremental one because once you unlock the capture upgrades, you can leave the game running in the background to grind for achievements and come back later to buy the remaining upgrades.