Leonardo is a new drawing and painting app that works really well with the SP4 (and all other Surfaces). It supports pen pressure, multi-touch and the UI scales to any screen size which makes it easier to to use with your pen/finger.
Full disclosure: I have developed Leonardo myself ;-)
These two are paid applications but both have infinite canvas.
madewithmischief - vector-based
Leonardo - raster-based but better... i think. Lol.
I am the developer of the drawing app Leonardo. I have a SP2, SP3, SP4 and two Wacom Cintiq/Companions (plus a bunch of non-screen tablets).
If you want it to be portable I would recommend a Surface Pro 4 or Surface Book. They are surprisingly good for drawing and much easier to take with you then the Wacom Companion.
If you will mostly stay in one place with your tablet the Wacom is however a better choice since the pen is a bit nicer and it have side mounted buttons.
Leonardo has everything you ask for. You can lower the opacity of the window (Settings > Window opacity) to trace something of the web or you can important it in to another layer. Leonardo also have perspective tools, some nice brushes and is very easy to use.
Full disclosure: I have developed Leonardo myself :)
its actually really decent. like a lot of other people here mention it handles office and onenote use and things like that.
however i have noticed that it chokes a little on too many tabs. i think for me 10~ is about where it starts to get frustratingly slow.
as for drawing, if shes doing raster with a reasonable amount of layers then its probably fine (for a REALLY AWESOME drawing app that is legitimately worth your money and is designed for surface I wholeheartedly recommend Leonardo ). If shes doing a lot of vector work a M3 is probably pushing it a little
Leonardo is pretty good for sketches and technical drawings. It has an infinite canvas that means you never run out of canvas space and a lot of Line modes that help with lines, circles, perspective etc.
Full disclosure: I have developed Leonardo myself :)
I agree that the Surface is amazing for drawing!
It's so good that I decided to refocus the drawing app I am making called Leonardo for the Surface. The one important change I hade to make was to add a scalable UI so that buttons and other UI elements become big enough be used with your stylus/fingers.
you're gonna need something more advanced than fresh paint, eventually. Definitely something that supports layers, and has a good touch friendly interface. Fresh paint has no layers, and does not support one finger pan, which gets annoying after a while.
The most popular app on this subreddit is Leonardo, but Sketchable is also good (search for it in the store). They are both very Surface friendly, but also beginner friendly. Other apps can be overwhelmingly complicated when you're starting out. You get a 14 day trial of Leonardo, but there's no trial for Sketchable so you'll have to check out the tutorials to get a feel for the premium version.
If you can't afford to buy one, you can try Mischief or Sketchbook pro (the desktop version!). These are the only (slightly) tablet friendly apps that have a free version that includes layers. Mischief won't cut it for long though, it's very restricted due to the vector approach, and so you can't do much with it.
edit: someone said that sketchbook pro doesn't have a free version anymore. Haven't checked it out in a while, so might be true.
Not free, but the app Leonardo is only $40 while in beta (there's a free trial you can check out) and it's well worth the price tag compared to comparable programs. http://www.getleonardo.com
It's pretty fantastic even in its early beta - it's photoshop-like without all the bloat and focused specifically on the drawing tools of photoshop (without all the photo editing, color correction, and other tools). My favorite feature is the control it gives you over brush stabilization and smoothing, great flexibility.
It's currently available for PC, not sure when the Mac beta opens up