Personally, I am using one of my laptops exactly as you described only at home secured network and only for important things, no browsing, downloading or anything. Still, during banking session, we can be infected so you never know but in the last few years I wasn't hacked even once so maybe it works. I hope Wink.
Added to the list: If possible try to use one computer only for banking and other important things (no email, no browsing, no downloading programs or open attachments on this machine) for all online activities use a different computer, with no important data.
Thanks again for this suggestion @Cryptovigi already added to the list as "Never leave your network unsecured and try to make the WIFI password extremely strong."
If anybody knows any other way how to secure the computer or stay safe online, please share.