I use Goodbudget. The appeal is that I can enter expenses from my phone, and my partner can do the same, and we can both see how much is left in each budget category. If we were to switch to a self-hosted version, it would run on a home server, but it would be accessible from anywhere. I don't think this is an option you considered.
Additionally, even if you use a third party host, it seems less likely they'd be snooping through your application data, as it would provide no benefit to their business of selling you hosting infrastructure. The providers of a budgeting app, on the other hand, have many reasons, benign and possibly not so benign, to be looking at your data.
Additionally, even if you use a third party host, it seems less likely they'd be snooping through your application data, as it would provide no benefit to their business of selling you hosting infrastructure. The providers of a budgeting app, on the other hand, have many reasons, benign and possibly not so benign, to be looking at your data.