Can't download anything with enough storage?

You actually don't have the required space.

Apps are shipped in containers called IPAs. An IPA is actually just a zip file, and compresses some of the content. Each app, depending on how they are built, can achieve varying degrees of compression.

In the above image, you can see just how much disparity exists between the App Store's reported size and the actual install size.

Infinity Blade 3 is listed at 1.7GB by the App Store, but installs to 2.6GB. Additionally, Bastion reports requiring 534MB, but actually needs more than twice that amount of space (1.2GB).

Since it would be impossible for Apple to gather the required information from actual install size, they offer the size of the IPA as a guideline. To be safe, one should allow for 3x the existing space. In your case, you may require about 800MB free (ballpark).

And remember, you need some free space (for caches, app data, etc.). It's unwise to operate with absolutely no free space, typically leading to a negative impact on performance.

Delete something you don't want to free up a smidge more space - assuming it's not a bogus error message.