Very familiar with updating to iOS7. Have done that a lot. Don't worry, I'll do a good job.
Not sure if you are aware of it, but there are several levels of thoroughness in updating an app to run on iOS7 and compile on Xcode 5.1.
a) Minimal - Fix the compiler errors so it compiles on Xcode 5.1, runs on iOS7. However, the layout may be messed up because of differences between iOS6 and iOS7. It will run, but will look bad!
b) Medium - like minimal, plus fix the obvious layout problems so it is back to decent looking. However, the design may still not take advantage of iOS7 features. It will run, and will just look ok.
c) Advanced - like medium, plus re-designing certain aspects of the user interface to optimise it for iOS7. Certain features, like preferred fonts, were only introduced in iOS7. We may suggest some changes to make the user interface more elegant and take advantage of such features.
We go the extra mile and do type (c) updating for you, for maximum satisfaction. Choose us if you'd like advanced updating.