How to store cryptocurrencies safely? How paranoid should you be when storing cryptocurrencies?

1. I am currently storing some BTC and LTC at paper wallets, but this does not feel good because what if the paper wallet gets 100 transactions in? Won't the paper wallet then be "full"? What if I accidentaly missed one character when I copied the private key by hand?

2. What if I import the private key to my Bitcoin-QT wallet on my computer in order to spend some BTC. When I am done spending the BTC I backup the wallet.dat on a USB stick, then I remove the wallet.dat file from the computer. The file will still be on the HDD and what if someone gets their hand on my computer and runs some recovery program that recovers the wallet.dat file?

I have soon 10 000€ stored in cryptocurrencies and losing them would suck so hard. What if someone comes up with a backdoor in Windows that steals everyone's wallet.dat file? I am sure there are people working on something like this, since they would be millionares if they succeed...
I agree this may be a duplicate question, but fundamentally you probably need to understand what is going on to understand what is at risk.

The blockchain is where the record of of your bitcoins are kept - they are not "on your computer".

What is "on your computer" is a set of keys which allow you to "approve" a transaction to move Bitcoins from a specified address.

There are two keys:
Private Key
Public key.

The private key is used to generate the public key, so as long as you have the private key, then you have the ability to:
a) create a public key
b) sign transactions

You cannot derive the private key from the public key - that would break all cryptography!

You do not have to do this with the Bitcoin QT client - there are other alternatives, Multibit being a good alternative as it is very quick to syncronise, and you can upload private keys easily.

If you keep only one copy of that private key - then you may have a problem if it gets lost or destroyed.

Therefore you should keep multiple copies.

To answer your question specifically - if you do not copy the file correctly you are screwed. If your computer is hacked, you are potentially screwed.

Checkout the link in the comment from @frisco for more information.