For a system you want to do banking :
1. Forget about Windows 95/98/Me. You should have atleast Windows 2000 or XP
2. Install a good firewall like Agnitum Outpost or Comodo.
3. Install a fast antivirus like Avira or avast!
4. DO NOT USE Internet Explorer. Use Firefox 3.0 or Opera 9.51
There are packages that come with antivirus + firewall (like F-Secure, PCCillin, Panda etc), but I dont consider them safe enough. The Firefox browser checks every website you visit for fraud(phishing) and shows warning if it is fraud. Also do not save any passwords in your browser.
I hope you find this information useful