60 cds isn't that many so you'll easily fit them onto an iPod. The smallest "proper" iPod the Nano has 8GB of memory and that can hold around about 2000 songs. So guessing at maybe 10 tracks an album that's 200 CDs.
However......
The "standard" way of copying a CD onto an iPod makes a copy that isn't as good as what's on the CD. It's close and through a normal pair of headphones you probably won't be able to tell.
However if you plug the iPod into a decent docking station or stereo then you'll probably be able to hear that it doesn't sound as good as it does when a CD is played.
So you have to turn up the "quality" of the copy, which takes up more space, so you probably wouldn't manage the full 2000 songs on an 8GB nano.
As a rough guide I do copy my music at a pretty high quality and my iPod's got nearly 7000 songs on it and is using about 55GB of space.
So I've got about 3.5 times as much music but it takes up nearly 7 times as much space. So each track takes up about twice as much space, so at a decent quality an 8GB nano might only hold 1000 songs.
A real audiophile would probably still turn their nose up at the quality I record at and would fit even less tracks on their iPod.
However to me, through a decent sound dock, it sounds great.
So basically do give some thought as to what size of iPod you get and a rough guide might be to halve the number of tracks that a shop tells you will fit on it.
Aside from a Dock if your stereo has the right inputs (ideally two "aux" jacks in the back) you can get a cable and plug your iPod right in to it. An example is this:
www.amazon.co.uk/Xxion-Value-Stereo-Cable-Connect/dp/B001QOX1SM
Any other advice?
Well the normal way for an iPod to work is to copy everything in your iTunes library from your computer.
So if you add something it's automatically copied to the iPod and if you delete something it's automatically deleted from it.
With lots of music that means that you have to keep all of your CDs on your computer which can take up a lot of space.
It's better to put bigger iPods into a "manual" mode which means you have to copy the music to your iPod, which is just like dragging a file around, but also means than when done you can delete it from your computer and get your space back.
So just keep that in the back of your mind and ask again later if you need any help on that.