As a composition sketchpad, I’d recommend korg gadget (if you like reason), modstep (if you like ableton live), and auria pro (if you like pro tools). Cubasis can also work, and gargeband is free IIRC (not using garageband myself).
I’d advise caution when purchasing iOS music apps as most of them are really limited or not-so-good sounding or both. I’ve amassed quite a collection of music apps that I never use after the initial honeymoon phase has passed. The inability to properly demo apps sucks on many levels.
As for synths, my favorites are Virsyn Tera, Moog Model 15, Sunrizer and the Korg iM1. These are all solid, fully featured synths/workstations that sound usable. While there are other apps I also find myself using, these are the ones I can recommend quite strongly.
For proper processing (ie comparable to a computer), Auria Pro has most of the fabfilter plugins available as in-app purchases. So if you use and love fabfilter stuff on the computer, Auria might be a good investment.
Like someone mentioned, Audioshare, Audiobus and AudioCopy/Audiopaste are all very useful tools in the iOS audio toolbox.
One more word on samples - they can be a bitch to manage on the iOS, as access to a common file system doesn’t exist (without jailbreaking). Personally I am still figuring out which app I want to use for building a sample library for, since there is very little point in copying the same 100’s/1000’s of samples into many different apps.