I'd recommend anyone looking for their first job out of university to consider strongly a job at a startup. Consider it a 'finishing school', where you'll have the highest chance to touch as many different technologies and tasks as possible (from system administration, to backend to frontend work), as opposed to the 'Big Company' where (especially for a first job) you'll be focused on one task. The important thing is…
I went about it the opposite way, and can definitely recommend that as well: big company first, then small. The big company experience shows you a ton of things, like how to interview, build, and deploy at scale. The small company can benefit from your ability to bring order to chaos, develop tools which are obvious in any big company but strangely missing from every small one, and more. Maybe it doesn't matter which…
It's important to differentiate skills learned at big companies. Some are very useful, but others are coping mechanisms that have no place in a startup. Meanwhile, the scrappiness and well-rounded skill set learned at a startup will almost always have a place in larger businesses.
My own personal recommendation for early career workers would be to prefer the cream-of-the-crop mid and large companies where you'll get useful experience you can't find anywhere else, then prefer startups and leave the slower-moving and more dysfunctional larger companies as a last resort.