Have you ever received bitcoins, or did you just install the software? That is the first question you should answer before proceeding, you do not want to lose previously received bitcoins by making an error. The wallet data stored on your computer is the only way that you can spend bitcoins you previously received.
You don't describe which wallet software you installed, but whatever it is, the software itself should be upgraded to the latest version if it is several months old or more.
Bitcoin-Qt wallet software does not remove a user's wallet data file even when it is uninstalled and reinstalled. If you start it up again, you will see the same addresses and be prompted for the same forgotten password. You will need to manually delete (or rename) the wallet.dat file in order for the software to create a new blank wallet.
https://en.bitcoin.it/wiki/Data_directoryOther wallet software such as Electrum will store the wallet data in different locations.
Before you worry about hackers and secure storage and whether you want a second computer just for Bitcoin, you should simply familiarize yourself with the Bitcoin wallet software.