Wow, some of the responses here have been pretty complicated. I'm gonna suggest starting simple.
A medium sized gun is going to be a good starting point.
In a semi-auto, that would be something like a Glock 19, CZ P-07, Walther PPQ, and many others. I say stick to 9mm, as it is cheap and will allow you to practice more often.
If you want to go for a revolver, I would say a .357 in the 3"-4" barrel range. You can run cheaper .38s through it for practice, thus, once again keeping cost down.
The reason I recommend going with something mid-sized is because it will be versatile. It will be large enough to be a good, controllable learning gun, but small enough to be concealable, should you decide to go that direction in the future.
With a budget in the $1000 range, you can either get one expensive gun, or two less expensive, but still very nice guns. Better yet, you can get one good gun in the $400 - $500 range ( lots of options -just take a look at budsgunshop.com and you will see lots of very good guns in that price range), and spend the rest of your budget on lots of practice ammo and more training.