Which tool to use for "home banking"?

Probably the most powerful solution you can use is GnuCash. It's not the easiest to learn, but there is quite a bit of documentation available to teach it, and it has a lot of useful features such as double-entry, hierarchical accounts, and the ability to import from Quicken. The GnuCash developers have specifically stated that they will not take on the responsibility for encryption, as it goes against their philosophy of making a program do one thing well; but they state that they are in full support of using encrypted file systems to store your data.

Homebank

Homebank is, as the name suggests, a home banking application. It targets home users rather than businesses so seems well suited to your need.

As far as encryption is concerned, I don't think this is an inbuilt ability. However, you can keep all of your files in a particular folder and encrypt that separately. An encrypted /home might be useful for this. Homebank does allow you to set the default directory for its files, but does not appear to stop you putting them in other, less secure, places.

See also, this related question.

Grisbi is what I use, and I really find it easy and full-featured.

It allows for crypting your files if needed.

There is also kmymoney