I would like to build a graphical application that must work on at least Windows, Linux and MacOS. I would like to know what do you suggest I should use.
I have some experience with Java and C++ but I thought about using Java Swing first. What do you think or further suggest (like maybe tools or frameworks)? I also may be needing to connect to a PostgreSQL database to store data.
Java is probably the simplest way to get your application working on all 3 platforms as well as to add database support. All of these are equally possible in C++, but it definitely involves more work because you need to learn to use a cross-platform widget toolkit. Also, C++ database drivers usually have wildly varying designs but Java presents a unified interface via JDBC - this also means that you can change your underlying DB at any time without having to change your code.
wxWidgets does cross-platform easily enough, using available native toolkits. You could probably use a ORM for the database part, but I don't have enough experience using them under C++ to provide an actual informed opinion there.
GTK is cross-platform. Pidgin uses it and manages to get away with being generally considered a fully-cross-platform app. The installer size is a problem, though.
I would suggest Qt too. Qt has seen very good development recently, their examples and documentation base is quite large, and the LGPL license is flexible too, for creating proprietary software. It has a good Qt Creator IDE, a Qt GUI Designer. Plus is has quite a number of modules, enabling it to be used in conjunction with other language developed apps/libraries. And, it is used in commercial/public apps like Google Earth, Skype (maybe only the linux version). So, it has a good history of reliability. And yeah, for Database, it has modules, like Qt-Sql. Another advantage you get over java is speed.