I just discovered the Teebird which I love but I can't throw as far. Am I better off trying to work on my mechanics with a Teebird, or a slower driver like a beast? Any other driver recommendations?
A Teebird is perfect depending on how long you have been playing. Personally, since you aren't throwing extremely long distance yet, I'd have to recommend something along the lines of a Leopard or Cheetah, which is a bit less stable than the Teebird, but both can still be thrown for well over 300' with the proper technique. The reason you should invest in those two fairway drivers over the Teebird is that the Teebird is still a pretty stable disc, and will mask certain bad habits (OAT, etc) that you may have. And because it hides these problems, you'll continue throwing with the same technique as you currently have, and subsequently not increase your distance much in the mean time.
The Leopard and Cheetah be able to give you more insight into what you can change/improve upon to make your drives longer and more consistent since they are more responsive to bad technique than a more stable/overstable disc. Throw these instead of your Teebird, and learn how to throw them well. Then, once you are consistent with them (good accuracy and precision; 300' or greater drives; little to no "whoops" pop-fly shots, etc.), break out the faster discs such as a Teebird, Sidewinder, Valkyrie, or other slightly faster drivers.
One of the best things that you can do though, and this may sound strange, is
learn how to drive with a putter. A putter will be the most responsive disc (except for insanely overstable putters such as the Pig and Zone) you can drive with that can help visualize your flaws and aid you in improve your game. Find a Wizard, Magic, Aviar, or whatever you use to putt, go out to a field and start driving with them. If they turn and burn hard right, you've got OAT issues, etc. They are the master of diagnosing driving illnesses.
Last but not least (actually, do this prior to throwing another drive).... watch some of the YouTube videos of driving technique. There are a couple that I recommend to everyone; More Snap 1 and 2, and the Dan Beto Driving Tips and Technique. These will help your drives more than anything else, especially when paired with a fairway driver that you can adequately handle.