Cryptocurrency Storage Question

Hi everyone, question for the more advanced crypto traders (and storers):

So I do not want to leave my coins on the exchanges (look what just happened in Japan....), so I purchased a Ledger Nano S. It works great and have zero problems, with the exception of 1 thing: only seems to hold 4 coins at a time? Well that is not good if you have multiple coins. So what should I do?

1. buy multiple Ledger Nano S and/or Trezors?
2. Software/Desktop wallets?
3. Leave on the exchanges?

When it comes to the software wallets - my big concern is this: if it exists on your computer, what if your computer gets compromised. What if it gets hacked? What if it crashes or dies? What if you need a new computer? What if you bring your computer into a shop for upgrades? What happens to your coins?

The lazy way out is just leaving them on the exchanges . . . . but I really want to go the software route, but am completely confused as to what to do.

Thanks for your help!!!!!!