Thanks for everyone's reply's, especially about creating a bitcoin address and key offline.
I intend to store these bitcoins long term, and buy them as and when funds are available.
The reason I asked about generating a new bitcoin address each time I purchase bitcoins, is because I thought this would be much safer with Paper Wallets? Am I wrong in thinking this? I fully intend to store my paper wallet where no one will ever find it, but if someone did, they would have access to my entire bitcoin balance, as opposed to me hiding several paper wallets in very different places. Does this make sense? Spreading my balance between several addresses?
Thanks again