Just to follow up on this, what's the best way to transfer everything from my current SSD to the new one?
Assuming the old SSD connects via SATA, and if your PC/laptop has a spare sata/power connection, you can disconnect the old SSD, hook up the new one and clean install the OS on it. Power down and reconnect the old SSD. When you boot you will given the option to select which disk to boot from. Choose the new one.
You should then be able to access all the files and folders from the old SSD and copy/paste them over to the new SSD - this will give the fastest transfer speeds. If the old SSD has a decent capacity you can then format (wipe) it and retain it in the machine or shove it in an external enclosure as Welshred has suggested.
If you can't connect both SSDs, or if the old SSD is too small to be useful, high capacity external hard drives are ~£80-90 for 4TB. A USB3 model will give better transfer speeds if your PC/laptop has a USB3 port. Always good practice to backup your stuff so potentially a worthwhile investment if you don't do this already.
Cloud storage is another option - most companies give a few GB 'free', but it can get expensive for larger amounts of data (£80+ a year for TB scale storage). It can also take days to upload/download depending on your files/internet speeds.