Suppose I pick my 30+ year old Amiga floppies from the basement. Any chance that there are still readable? what would be the simplest way to copy the content on a modern storage so I could inspect them on an emulator.
There are two popular USB floppy drive controllers for archiving Amiga disks: KryoFlux and Greaseweazle. You need a standard disk reader to use along (not a USB one).
The KryoFlux is a bit more expensive but can create complete archival level images (called KryoFlux stream). Otherwise both devices will produce floppy images (ADF) that can be used in any Amiga emulator or written back to floppy to use on a real Amiga.
Here's an overview of the available tools, some of them are pretty old, you can't go wrong with the two I listed above: https://www.amigaforever.com/kb/13-118
You can easily convert to other formats with the HxC Floppy Software.
For the Amiga you have some really good options, I would personally recommend getting a standard PC 3.5in drive and a GreaseWeazle floppy controller which adapts it to USB with extreme low level control for reading disks.
This will also allow the WinUAE Amiga emulator to directly read the disks in the drive!
Note that while GreaseWeazle is an awesome project, I have had more luck reading floppies with the actual Amiga.
I suspect it would help to use a DD FDD like the one the Amiga has rather than an HD one.
However, considering you have to build your own custom Arduino board or be on the waiting list to buy one, it's a bit more complicated than "Just buy a simple USB floppy drive for 15 bucks online".