Paper by Fiftythree is a favorite and Bamboo Paper is a good basic note app. Fiftythree has more features, even in the free version. Definitely worth trying Paper by Fiftythree!
I have an older iPad 2 and both of those apps are fun to use and have saving and sharing options. Fiftythree has a Pencil stylus and it’s cheaper than the Apple Pencil. I don’t have either of those pencils, so can’t personally recommend either. I’ve heard great things about both. I believe their “smart” features only work with newer iPad models, so no excuse for me try try one yet. I use just a basic stylus and it is still enjoyable.
Check out http://www.fiftythree.com for their Paper app and Pencil. If you have a larger budget, I hear iPad Pro and Apple Pencil are awesome.
I tried several iPad note apps, mainly just for taking handwritten notes or playing around. I kept going back to Bamboo Paper. More recently, I tried Fiftythree and really like it even though I have only used it a little. I can see it becoming my fave down the road. Catherine Madden makes it look easy: http://youtu.be/phCuOiPtX7o