Good practices for organizing notes As a PhD student I generate a lot of pages with calculations, ideas and lecture notes.

Most of them are useful only for a short amount of time, but some may be important for much longer (when writing a paper, or when having new ideas to continue a once abandoned project). Typically I work on a few project simultaneously.

The question is, what is a good practice of taking and keeping notes? (With or without computer apps.)

Writing on single sheets (even if adding date and title) makes it easy to organize by topic, but also easy to loose. Keeping in one notepad makes it harder to collect useful things of one topic in one place.
You should keep a research notebook, regardless of whatever other system you have for notes. The format of the notebook is up to you; it can even be public (see Carl Boettiger's as an example of an electronic lab notebook). it can be created in programs such as an iPython or Jupyter notebook, or even a more specialized program such as Findings.

If you choose the pen-and-paper route for your research notes, and want to have the added flexibility/security of taking your notes with you (and also because it's good practice to do so), you should consider getting a scanner and making regular backups. You can then import these into a product like Evernote, Onenote, or MacJournal,
If you are using LaTeX, your options are somewhat limited, as most of the major tools for notebooking really don't support "live" LaTeX. Then you'd be better off using something like Aquamacs as a holder for your "notebooks" (LaTeX documents), and then using one of the above packages (or something like Papers or Paperless to organize the resulting PDFs.