Any notebook will do for your writer's journal. You can use a spiral notebook or composition book from the school supplies section a t your favorite store or visit the bookstore for a selection of blank books. The variety is impressive, from lined or unlined sheets to various sizes (and shapes). The important thing is that you feel comfortable with the book so you'll enjoy writing in it often.
You might even prefer to use your computer to journal. Many of my writing friends insist this is the best method because of the "search and find" features on most word processing programs. I prefer a portable, handwritten journal. If this is your choice, too, choose a writing instrument with as much care as the journal itself. Do you want to hear the scratching of a pencil or marker on the page or feel the glide of a gel-ink or fountain pen? I like the feel of smooth, thicker paper and the fast, flowing ink of a Roller Ball. But, I also prefer different colors to help me designate different days at a glance. The choice is yours.
Whichever method you choose, be sure to keep the first few pages blank. Record favorite writing exercises or prompts on those opening pages. You'll be able to quickly find writing prompts whenever you want to write during unexpected spare time. Each time you complete an exercise, you'll gain something more from it. Draw from these completed exercises, just as you'll glean from experiences in each journal entry in developing writing ideas.