Hi Raptor 88,
It worked once I removed the old hdd from the computer. I didn't know I had to do that, I thought that once I had changed the boot order in the bios that Windows would boot it from the SSD and I would be able to erase the old hdd, but that was not the case. You really have to unplug the old hdd for Windows to adopt the SSD as the system drive.
I have an external hdd docking station, so I just used that to wipe all the partitions on the old hdd and created a single one. I used EaseUS Partition Master to do it, which is free (just had to be careful not to install the other software that they try to force you to install). Although I think you can do the same with Disk Management in Windows.
Thank you for the tips about separating the system from the data, it really makes sense and I will adopt it.
Also, many thanks for all the support given to me during the whole process!