Go ahead and make online purchases from known sites. These sites have secure ecommerce systems and measures in place that create a safe environment for shopping online. What you need to do is to be wary of purchases from dodgy sites and also direct transactions with buyers and sellers found on forums and auction sites. When you make those sorts of transactions, be careful of sharing too much banking information with them. Other than your name and account number, they do not need to know anything else.
In summary, keep your PC updated, install a strong anti-virus system and be extra-aware when online. Ignore suspicious requests, only connect to banks from safe spots and deal with strangers cautiously. Follow these steps and you will be safe from cybercrime. Share these same tips with everyone in your home that has an online bank account.