For watercolour, my wife has a little plastic paint tray/box that accepts blocks of paint. She has a malleable eraser in a small plastic box that slips inside the box neatly. She also bought a water brush so she doesn’t need a cup of water.
For sketching, she likes ink and so just carries around a selection in her pencil case. These will include a fine marker, but mainly she uses around 5 refillable pens with different nibs and whatever colour ink she likes at the time. She uses the water brush with these, too.
For paper, she buys decent art pads, postcard size.
Most her drawing now (the last 2-3 years probably) is done on her 9.7" iPad Pro with Procreate, though, because it’s no fuss and always there. It’s like that thing about the best camera being the one that’s with you, well she always has her iPad and Pencil nearby, so she just opens up Procreate, chooses her brush and gets going.
If you want to know any specifics, let me know and I can have a look when I’m at home.