Run Adobe CC = macOS or Windows, NOT iOS so no iPad will do the job unless all you need is the lightweight Lr companion app. If you need the full power of Ps, Lr, Ai, and/or Id then no iPad will serve.
$1000 budget + macOS = basic 13" MacBook Air, period (unless you find an older model used).
Truthfully, you'll find better performing Windows devices for less money. The 13" MacBook Air is a dual-core i5 machine in a standard notebook config. With a $1000 budget you can get a 13" Dell 2-in-1 an i7 and matching RAM. The Dell has a touch screen will fold over to act like a tablet. For $50 over you budget you can get a similar Dell that's 15". There are many many other options.
I certainly prefer my 27 iMac or MBPr for design ( I'm a complete noob and only do very small stuff for myself, GF is a professional artist ) work. I swore off PS several years ago and now live by Pixelmator and Affinity software ( https://affinity.serif.com/en-us/ ).
I'm assuming the OP wants a Mac or wouldn't be posting here.
Setup sounds similar to mine. I have an iMac 5k on my desk for the heavy lifting, and the "satellite" machine is an 11" MacBook Air. It's plenty fast enough for my CC mainstays (Photoshop, Illustrator, InDesign), but the screen is on the small side. I'd say a 13" MBA would do you quite well if you don't mind non-retina display. Buy refurbished from Apple and you'll save a a couple hundred dollars right off the bat.