I see you're based out of NYC. Depending on your overall level of experience with blue water (snorkeling, swimming, etc.) - you may not need the additional safety net of a private DM. Have you done drift dives before, boat dives, or just shore dives? If you've done all three, you probably don't need a private DM. If you've done boat dives and shore dives, it's a tossup.
What I WOULD suggest is looking at the planned dives carefully. Usually the first dive is around 75-85 feet and the second is around 65 feet. Although the dive schedule may show different, shallower, depths like, say, 65 and 50 feet. For a brand new diver, that first morning dive can be a lot to manage if you don't have experience diving deep in a drift dive. You may want to skip the deep dive your first day or two to do the shallow dive to get a little confidence, dial in your weights with your planned gear, etc. Maybe if you want to up your dive count, go on the shallow afternoon dive if there is one. A DM supporting you for the deep ones may help, but it may also become a crutch too easily. YMMV.
Some may disagree with my depth numbers, but my computer from last week certainly doesn't - and I stayed with or above the DM all week.
I wouldn't add in shore dives as a new diver to Coz. Relax instead. Snorkel. Find your zen. At MOST use a shore dive to help you dial in your buoyancy and watch the current.
I'm mostly in rental gear (but fixing it for October). However, mask/fins/snorkel (YES SNORKEL DARNIT)/computer/DSMB should be the minimum you own and know how to use before you go. If you plan to do a night dive - buy a light. The Wurkkos DL08 is on sale RIGHT NOW (for the next 24 hours or so) on amazon and is better than the one the dive shop gives you for a night dive.