Where do my downloads go?

It's in your iTunes library. Even if you get a new computer, you can download it again for free. iTunes has the apps that you buy saved under your Apple account. When you get your phone, syncing it with iTunes will add it to the phone or you can just directly download it onto the phone. After clicking, buy now, it will say you have already purchased it and won't be charged again.

 

In iTunes, you should now have an Applications entry in the Library Source list on the left - this is where you can see all of the apps you have downloaded from the App Store. Technically, it's stored in your iTunes Music folder on your PC. I have a Mac and I'm guessing the file structure is different than it is in Windows when it comes to how iTunes handles this, but I have a Mobile Applications in my Music folder where all my apps are.

Don't move the apps around on your hard drive or anything - all installation and upgrading is done through iTunes automatically and moving apps will only confuse it.