If I were you I would look for the Surface Pro line up. The current model doesn't come with the pen and the keyboard but with the 2000 budget you can purchase them separately. I would go for the middle specs (i5, 256GB SSD, 8GB ram) but with your 2000 budget you of course can aim for higher specs (i7, 512GB SSD, 16GB ram will be sweet).
LOL I didn't read your explanation further after seeing your budget when writing my previous post XD
Yeah, mines works well with my tablet! But then again, it's somewhat small so I wouldn't really know if it depends on the size or not
Are you specifically looking for a laptop or just a computer in general? Building your own PC would definitely give you the best bang for your buck if you're on a budget but for those like me who rely on being able to move from place to place, a laptop is the next best thing.
I'd say the specs you need to keep a look out for are the processor (intel i5/i7), RAM (around 8GB is a good number) and the GPU (I personally prefer NVIDIA). I also used to dabble with video editing projects so I tended to go with "gaming laptops" too because they basically had the same needs (that, and I love me some Overwatch lol). Other non-gaming oriented laptops can also advertise that they have the same specs but have less powerful cooling systems so overloading them would result in a fried motherboard.
Definitely do not go for anything below an Intel i5 (sorry I'm not familiar with AMD units) processor if you're the type who likes to have many programs open at once. Good brands I know of are ASUS (ASUS ROG if you're looking at gaming), MSI and Lenovo. I also owned a Macbook Pro and the only advantage I can say it had over Windows laptops is the retina display. The specs just couldn't compare in terms of value though. :<
It'd be great to find a buddy who's into computers when you go shopping so you can pinpoint the best deals. In my experience, buying from malls was slightly more expensive than going down to the computer stores directly to compare prices. Sorry for the long wall of text and wishing you good luck in laptop hunting! 
When I was looking for a new computer, either a laptop or a stationary one, I got the recommendation of looking for a gaming computer.
The reason:
It's got a good memory, nice graphics cards and everything else needed for gaming including a good cooling system.
Drawing, takes just as much memory from the computer as gaming, which is why I was recommended that!
You'll want to ensure the laptop has at least 8gb RAM, considering that you are doing digital art.
If the art you make is pretty heavy (in that you use millions of layers on large files often), you might want a little more RAM, but the general consensus is that 8gb RAM is a good amount for general art.
ooh honey with a budget like that, youre in for a treat
for your looking around, some specs. you will need:
a lot of computer-buying sites categorise their laptops like - 'for casual use' 'for office use' 'for HEAVY use (dun dun dun!)' - for drawing, believe it or not, you want that last one. you want the kinda hardware animators use.
personally, i recommend checking out lenovo.
i have a lenovo legion, which is a gaming laptop, and its like... $900? im not american, so im not 100% but its jus below the 1k mark. thats considered budget, weirdly.
because its made for gaming, its gotta be Powerful - and it is! i7 processor, 8gb of RAM, a v nice screen to boot. i can run so many things at once and it still runs cool, i havent experienced it crashing on me once. i work in CSP and sometimes i get lag, but i think thats more of a csp thing than a laptop thing. gaming laptops are p trustworthy for drawing imo, bc theyre used to smth even higher caliber - but theyre a bit ugly 
when i was looking around, i was eyeing up some other lenovos for higher prices that are even nicer (and slimmer and prettier) - so look around!
i recommend going into a shop and getting your hands on some different models to see how they feel, as well.
Same with my Dell I bought a couple of yrs back. My list of requirements was that I wanted it to be 17"(I'm getting old & dont care to squint at the screen when I'm working on art- plus I had bought a 23" monitor for my desktop and I really liked looking at my art on a larger scale), needed a lot of hard drive space(this one has 1TB), a decent amount of USB ports(3, plus I have an HDMI port as well), and more memory than my last laptop(has 8GB capacity). I got this one for under $600 during Black Friday, so I'm happy with what I got.
I stuck with AMD. I put my 1st desktop together using AMD and had no issues with it(processor wise) for years.
the lenovo yoga i have is really good with an i7 processor and being lightweight but with a decent sized screen.
Oh yeah, the driver. I had to clear out a bit of files for that but it's a good thing they were old and I wasn't using them anymore.
Oh my gosh, thank you so much for the tips everyone!
I didn't even realize I could look at gaming laptops but in retrospect it makes perfect sense. and with those I don't need to worry about a pointless touchscreen being a thing. Even if its hideous I can always pile a bunch of stickers on it so thats not an issue.
Maybe sometime in the future I can try and make myself a custom hard drive.
Is there a good time to buy laptops aside from Black Friday or is that a thing that changes between brands and companies?
@Stardust-clearwater With the whole "Back to School" sales starting up, you can start looking at laptops now as they do have some sales going.
wow for $600 it's really a bargain 
and yes I also like to work with an external desktop screen when I don't need to move around. I'm sure there are a lot of choices but I guess my choice is a bit biased because I also play games and stuff and the Asus I'm borrowing is like 4 years old and it still runs like a beast without any issue.
