I think that you should definitely get the manual transmission. Learning stick isn't the toughest thing in the world, but it helps to have somebody that knows what they're doing to teach you. For info on driving a stick, try searching for something like "learning stick" I came up with these:
We can help you with more specific questions. For your mod for 500-600 bucks, I'd go with some better tires. If you had 800-900 you could go with 17" rims and even better tires (i.e. Rota rims w/ Kumho tires). I don't think there are any other mods for that much that make as big of a difference.