For design stuff? I'd recommend the two laptops I've had but they have discontinued the models... figures lol. The first was a Samsung (actually that was the gaming computer, I always mix them up but it was a powerhouse) and my second is an Asus. I love my Asus one - I think it cost around $750 after tax but I know there was a sale running when I got it. It starts up really fast, faster than my Samsung did and there are times where I leave InDesign, Photoshop, Illustrator and Dreamweaver open at once for days and I can still stream Netflix without a hitch.
I have zero experience with Chrome OS computers but I've heard Adobe programs have issues with them. Creative Cloud runs perfectly on Windows though :)
I can't name any models off the tops of my head specifically but I know that Asus, Lenovo, and Acer seem to be trusted brands. I don't think you want to go below an i5 processor, i7 is nice if you can afford it. For Ghz, unless you're doing lots of crazy photo editing or video editing, I don't think you need anything higher than 2.5. They say 16gb of RAM is optimal but my computer has 8 and it's fine. There is a guy on YouTube, Roberto Blake (that's his username), who does a lot of videos for graphic designers and he's done a handful of videos about computer specs for designers and they are very insightful! I'd totally recommend check his laptop videos out :) His mini Mac rant in his budget friendly laptop video cracks me up.