Have you tried ProCreate? 10 bucks, one-time buy (no subscription)
It's a wonderful program with very low input lag, feels almost like drawing on paper.
https://itunes.apple.com/us/app/pro.....te/id425073498

Some others like Medibang, which is free:
https://itunes.apple.com/us/app/med.....d/id1003588804

For the case I am very pleased with my DodoCase. They're more expensive than most other cases but are very well constructed, durable and have a loop on the side for the pencil. There's a cover and a strap to so they look like a nice sketchbook when closed. They can also go kickstand mode if you like drawing at a 45˚ angle on a table. Worth it, IMO!

I tried an ipad pro for a while, but yeah, I couldn't deal with ios in the end. I still rather use my old Acer Aspire R7-572G for drawing even though the pen is objectively not as good.
By the way there's an entire forum dedicated to notebooks and tablets with pen support with lots of useful information: http://forum.tabletpcreview.com/

I love my iPad Pro, and I do most stuff in Medibang, which is free and works cross-platform. You can start stuff on the iPad, do a cloud save natively in the app, and open the same file on a desktop without the need for iCloud or Dropbox.

Have you come to a conclusion?
I'm in the same boat, same (about $400) budget.
One thing that I think might be useful is that Win 10 tablet can be "projected" on, i.e. function as an extra screen for a beefy desktop.
"Simulated" it with a laptop and Wacom connected: pressure sensitivity was working and latency wasn't noticeable.
The problem is for that budget, it's either brands I never heard of or entry-level tablets without a stylus included, all Atom. I'm really not sure how well it would perform for the common, lightweight tasks, especially a couple of years down the line.