lots of freebies here to do what you want. I use Audacity although it can be a little hard to get to grips with and you will need to download Lame.dll to export your audio.
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Forget trying to "store them on digital", you do not have the time it will take to play those records and cassettes, just download the tracks from the various streaming sites instead.
Far quicker and easier.

Then store them all. :)

I recently got some Bluetooth headphones for at work with the intention of using an old phone to send to them, asked my kids (youngest=22) for some music and they tell me that they now just stream it and do not store it.
No wonder my net bandwidth has to be unlimited.
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Welcome to reality. See if you can get added to their accounts; sometimes cheaper for multiple accounts than another single.
I was kind of coming round to the fact that it may be better all round to scrap the recorded music and stream it instead.

Now I just have to build up the courage to get rid of it all. [I can't...]
You don't need to. Just because you stream it, doesn't mean you can't have the pleasure (and the memories) of it sitting on the shelf. It reminds you of a time when life was simple, and just fun. When you looked at the sleeve, and thought about the time when you bought it, or the person that it reminds you of - something that the tech savvy kids of today will never have.