@NIrish -- If you're thinking of getting into bitcoin, by no means use an online web wallet. Download for example Electrum, and create your own wallet. Electrum will give you a private key that looks something like:

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xprv9uLTx27spgZJdqXogmUiHUm4XgWFxcc2zRki9A9aWur8vB 5hj3micsEd4VvJM4G3jsGPMRbi9HGJHs5mXE6crtGd25xGDP28 XjyuXjS96YD
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Think of that as basically the PIN code to your bank card. That's all you need, and you will always have full access to your funds. However, it's your responsibility to keep it secure and protected, as if you lose it, there is no bank to call. You just simply lose the money.

As long as you keep that private key, then that money is probably far more secure than in a traditional bank account. Nobody can touch it -- not any bank, government, nothing. It's yours.