Help needed :D (SSD)

As others have said, the first drive is the one you want - the motherboard will support either kind, but the second drive (in spite of being a higher price) is a SATA drive, and would not give you better performance than a conventional 2.5" SSD. Some motherboards will support only SATA drives, so those users would need to get the second drive, but since your motherboard supports both and there is a difference in performance, go with the first drive.

If the 90€ price is not too much, I would recommend going for the 512GB version of the drive. If you choose to install the OS on it, you'll want the extra space, and it will improve Windows performance in general (and boot time in particular). Even if you don't move the OS to it, given the size of Steam libraries (not to mention Uplay, Origin, Epic, GOG, etc.), I think you'll enjoy having the extra space. If you ever do stream/record your gaming sessions, it may also benefit from having a large, fast drive.

As Talgaby mentioned, your motherboard does not have a mounting post for shorter drives - you need to use the 2280 size (22mm wide and 80mm long - some drives are shorter, at 60mm or 42mm). That shouldn't be a problem, as it's the most common size, and both drives you linked to fit the 2280 format.

For game / OS start. Whatever you use, make a backup of your data before you work.

Data may be lost during extension work.