First, we need to define 'complete security'.
The only 100% secure machine is one that is locked in the bank vault, disconnected from the network, and unplugged! 🙂
IPSec tunnels would be a good option for securing bank traffic. Depending on the number of sites, you may want to consider a VPN concentrator; if yo don't have a firewall, I would highly recommend one for each site connected to the internet.
Internet access needs to be closely watched. If internet access is given, a zombied machine can be remotely controlled, and data leaked. A machine can be zombied in many ways, web install, social engineering, etc.
The fact that you're posting this question tells me you're not too slow! However, you may want to consult a partner if this configuration needs to be done rapidly.