If you're really worried (and have the resources), you could have one computer/device for your at home wifi, banking, work and email (plus a few other trusted sites) ONLY, and another device that you use for browsing random websites, take with you and use public wifi, go on holidays with etc (but that you don't access your email with)...
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.
...you shlould never to leave your network unsecured!!!...While setting the WIFI password, try to make it extremely strong ...
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.