Oddly, my experience is different. Have only had HP's the last 10 years - I shop in the business section at the website, not personal, less bloatware, better prices and specs. Agree on a minimum 512GB SSD, and 16 GB RAM. Personally, I like a 14 inch screen - as Goldilocks would say, 13 is too small, 15 is too large for portability. The HP Elitebooks are very light, less than 3 lb. I'm replacing my last one now with a new Elitebook, only because it's 6 years old and because HP had a solid replacement - more memory, better screen resolution, better graphics - on sale at half the list price. As it still works fine, I'm having a tough time letting go of the old one, though.
If you go Intel I'd lean toward i7 or higher. Had problems with i3 and some i5 in the past. And I've heard the AMD Ryzen chips rock.
No problem with Dell, though I know several guys who use them without issues.