I am often asked for advice on "best-of-breed" apps to do various things on the iPhone/iPad, and one of the most-requested apps is a drawing or note-taking app. I've just found what meets my needs best: Ink, available free at https://itunes.apple.com/us/app/ink-for-ios/id584654242?ls=1&mt=8.
Besides the fact that it's free, what makes it fabulous? Almost nothing, and I mean that with the highest of praise. Although I like other apps for more complex notes (info below), when you open Ink what you see is essentially nothing - a blank screen, ready to written on, with a little menu indicator at bottom right. That's it. No need to choose notebook, change mode/font/color/ink width, etc. Just scribble away. When you're done, pull up on the screen and that screen has been saved in your photo roll. Double tap on the menu indicator, and you can email it, clear it, and do some other sharing things. But basically, this is a note card that needs no preparation to use: just scribble and save. Absolutely fabulous! I'm putting this on my home page, perhaps even in the dock area. The only drawback: the current version does not have "palm rejection" - if you touch the screen with your palm or another part of your hand, that messes up the inking capability. I would imagine it'll be added soon, though.
Need something more full-featured? If I need to be able to make drawings as well as type, I personally like PaperDesk (https://itunes.apple.com/us/app/paperdesk/id367552067?mt=8, $3.99 for the full-featured version; https://itunes.apple.com/us/app/paperdesk-lite/id367563434?mt=8, free for the lite/trial version). It lets you do pretty much whatever you want, including recording audio and incorporating that as well as photos in your notes. The power of PaperDesk, however, means that it takes a bit of time to get going, while Ink is ready right away.
Hope this helps some of you with your decision.