Subdividing metronome: I recommend the BOSS DB-60, but there are many inexpensive or free smartphone metronome apps available.
Electronic tuner: I have a Korg AW-2+ I use, but again there are very many inexpensive apps out there. Just about all professional bassists use electronic tuners these days.
Notebook/pencil: I'm a big believer in taking notes and writing things down. These should be brought to every lesson.
Rosin: Rosin is technique in a can. An amazing amount of problems on the double bass can be solved with using more rosin or getting fresh rosin. I use Pops as a great option for all-around all-weather playing. Remember, rosin doesn't last forever. When it gets cloudy, brittle, and hard it is probably time to replace it.
Basic Technique: Simandl Book I. Still the gold standard for developing good left hand technique. For more advanced players and difficult passages, I move on to alternatives such as extensions, bar fingerings, and four-finger technique.
Thumb position and Beyond: Petracchi: Simplified Higher Technique. I was never really comfortable in thumb position until I worked through this book. Rather than emphasize named positions, Petracchi's focus is on hand shapes. I have found this approach to be endlessly helpful.