There is no right or wrong way to document your journal. You should choose a medium that you enjoy to make sure that you actually write in your journal, encourages you to do exercises and prompts (if you wish) and allows you to do an efficient review of your journal.
The only rule is to choose a medium that you enjoy: TYPE it, WRITE it, DRAW it, PAINT it.
Personally I use a notebook and pen. If you love the feeling of physically writing down your thoughts, a paper notebook or binder/filofax may be the best option for you. But if you struggle to write or have bad handwriting you might prefer an electronic option (like one note or day one) or if you are a creative type you may even prefer to use a sketchbook.
Over the years I’ve used spiral-bound notebooks with lined pages, hardcover books with unlined pages, filofax binders, and beautiful handmade journals. Small monthly notebooks and yearly notebooks. Short entries and long proses. Whatever you choose is up to you; just don’t buy something that you are afraid to you. Think of it as a work-in-progress, a messy unfinished project.
What do you use as your current journal or what are you thinking of using?