That's right, the #00 Philips head screwdriver will work fine for the screws on the bottom (make sure you replace them in the same locations they were in, and be careful as they are tiny and prone to escaping onto the floor, hiding under tables, etc.) and for the retaining bracket.
You will also need a Torx #6 to remove the lugs on the side of the HD, which hold the HD in the retaining slots/holes. (I didn't have one the first time I tried this and managed to get them off using a pair of needle nose pliers, but that was really so much hassle compared to using the right tool!
Be careful not to strain the ribbon cable connecting the HD and you should be fine.