Thanks both. I've got all my files now backed up onto an external storage but it's more my programs I'm wary about, especially Chrome which holds some vital information. Last PC I sold I logged out of it but it still remembered my login details and all my bookmarks and passwords which I wasn't expecting.
Your programs will need to be reinstalled once you have installed the OS on the new SSD i.e. you can't just copy them over.
Not sure what you are looking to keep in Chrome, but when you reinstall and log in (either to the browser or gmail) all of the personal stuff (mail, cloud-based docs etc.) should be there. Bookmarks/favourites might be stored locally so you would need to use the export option in Chrome to save them as an html file somewhere on your external hard drive and import them when you have installed Chrome on the new SSD.
If you have things like templates and settings that you want to preserve from other programs, most will give you the option to export to a separate file from where they can be imported.
If you dont want Chrome to 'remember' you on a given computer you need to sign out and choose the 'Remove an account option' and then click on the account you want to remove. This doesn't delete your account or any of your stuff, it just forgets the login details in that browser. You might also want to check that you have turned off the option to let it remember passwords. If you use Chrome in 'incognito mode' it will remember the account name but not your password.
If you a flogging a PC in future and leaving the hard drive in, it is probably prudent to do a secure erase - W10 Recovery has an option to reinstall the OS with a secure erase option which will delete/overwrite all your personal data.