You haven't mentioned which OS it is that you'd like to use so I'll split this up by operating systems. You did mention Windows Ink, so I presume Windows is your OS of choice but for the sake of completeness I'll offer the most popular options for both ecosystems.
One of the most popular options of late is to use Microsoft's Surface tablet. This tablet could be connected to a monitor, so you can draw and interact with the tablet and it would be mirrored on the monitor. This configuration would match your ideal setup. The current latest and greatest is the Surface Pro 4 but the new Surface Pro is slated to arrive soon.
Surface Pro 1 and 2 used Wacom digitizers and styluses but Surface 3 and newer now use nTrig's technology for the pen input. Surface tablets can also take advantage of Windows Ink
You may also want to check out the Surface Studio, which is like a giant easel/canvas for drawing, although this doesn't fully match your ideal setup. The Surface Studio also uses nTrig digitizers.
There ARE other options out on the market that are laptops and have digitizers on their screens but they are difficult to find and lead to even more difficulty ascertaining what level of precision they offer.
You can use an iPad Pro with Apple Pencil and an app called AstroPad to mirror a Mac's screen onto the iPad, whereby you can interact with it using the pencil and touch. AstroPad is designed specifically for drawing and illustration (in contrast to something like Duet Display, which just turns your iPad into touchscreen.) This is actually reverse to your ideal setup because Photoshop/Illustrator would be running on the Mac and not on the iPad. The iPad would just be a drawing tablet in this setup.
At present, the Apple Pencil ONLY works with the iPad Pro models. This might not change even in the future.
You can also get a cheaper, regular iPad and pair that with a Bluetooth stylus like Wacom Bamboo. I've seen this be a very effective tool for drawing as well but you lose out on tilt control. Also, the palm rejection is definitely subpar and may require you to wear gloves to draw so that your fingers don't cause accidental marks
So far I have mentioned styluses from 3 companies: Wacom, nTrig and Apple
Many have their opinions regarding Wacom vs nTrig so I'll leave that choice up to you as the internet is full of arguments for and against each one. Each definitely has its set of pros and cons.
The Apple Pencil is the relative newcomer to the market but its inner workings seem to be very similar to that of nTrig's.
Personally I prefer the lower (maybe perceived) latency/higher responsiveness of Wacom digitizers/styluses over nTrig, having tried out both myself. There is no real perceivable difference between the nTrig stylus vs the Apple Pencil. I do know that the iPad Pro reacts to input quicker than a competing nTrig Windows tablet would (down to Apple's optimization I suppose)
From personal experience with all three styluses, I'd say Wacom is the most natural feeling, followed by Apple Pencil and then nTrig.
All three offer tilt support and similar levels of pressure sensitivity. But of course with an iPad Pro, you won't have to worry about drivers and troubleshooting software issues like Wacom and nTrig can sometimes cause on the Windows side.
As far as accuracy/preciseness is concerned, Wacom styluses/digitizers suffer from a minor amount of misalignment/parallax effect where the point on screen doesn't exactly match the tip of the stylus. This is really minor and isn't distracting (atleast to me). nTrig styluses seem to suffer from wobble, if you draw at slow speeds
Edit: Added links