A joystick is now part of the system requirements however you can fly with a mouse. Be advised I only recommend doing that IF you have flown sims with a mouse before. If your just learning to fly with a mouse and learning Aces High those are two pretty tough things to do, in my opinion. Mouse flying is not as natural as using a joystick. A joystick will make learning the game much easier. You also don't need a fancy schmancy stick to start with. Get a basic stick with a few buttons and a hat switch for views, thats about the minimum you'll need. Once you get familiar with the game you can then deceide if you want a better stick with more buttons and functionality. Also when getting a stick goto a place where you can test fit the stick to see if it fits your hand and grip. You want and really need buttons and switches to be in easy reach of your fingers.
Remember you can always fly H2H free while you save up the money for a stick.
EDIT- oops forgot the harware part. Without knowing your system specs it's really difficult to point anyplace to find or fix the problem. Run DxDiag and post the results and maybe we can help with then.