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Using pen and paper for taking notes stands the test of time, but as you may be working online more now and in the future you may find it easier to take notes on your device as you watch. Bear in mind that phones aren't good for this though, and it's better to - if you can - watch recordings on a tablet or preferably a laptop. Phones are fine but other devices have bigger screens and you can do multiple things at once on a laptop.
Digital notes have some advantages over paper notes:
Safety: you're less likely to lose digital notes as you can easily copy them and back them up.
Searchable: Many note-taking apps let you can search for keywords and phrases to quickly find information.
Screen shots: Some note-taking apps let you save images, so you can take screen shots or save images
Sound: Some note-taking apps have text-to-speech capability, so you can listen to your notes
Accessible: You don't have to carry your notes around, as you can access them online
There are a few apps available to use for taking notes, some specialist, some not so specialist
Notepad. Notepad is a pretty basic text editor that comes with Windows operating systems. If all you're doing is typing text, then this is fine. In fact, it's probably good for taking notes during a lecture or recording because of its simplicity. You might want to transfer your notes into something a little more sophisticated afterwards however
Word or other word processing software is perfectly fine for taking notes. Some people swear by Word as a note taking option, some people swear at it.
Evernote is a specialist note-taking app, which you can also use to organise, archive and manage your tasks. Notes can be text, drawings, photographs, or saved web pages. It's available for Windows, Mac, Android and iOS and operates on the "freemium" model - a free version with limited functionality and a paid version with more bells and whistles. Notes can be organised, annotated, commented upon, search and exported.
OneNote is part of Microsoft Office but also exists as a free standalone version for Windows, Mac, Android and iOS. It does pretty much the same things as Evernote, with the exception of saving web content.
Google Keep is completely free to use with fairly standard note-taking features, but integrates well with other Google products
Simplenote has a clear and clean interface like and isn't as sophisticated as some apps, but is free to use
There are many other dedicated note-taking apps available, but what you use will depend upon your level of comfort using apps. The likes of Evernote and OneNote have lots of features but might be more complicated to use. If you prefer less complicated apps, Simplenote or even Notepad might be better options.