First, get certified.
This is actually a pretty good question. I had the same when I did my first OW after my certification in the Gulf of Mexico.
Yes, definitely tell them that you are a new diver when you make the reservation. Some charters may hook you up with a dive master, even if you have a buddy. Or, they may avoid dive sites that could be a bit much for you (current, depth, etc.) At the very least, they'll keep an extra eye on you.
I didn't have a dive buddy on my first dive. I just booked a slot on a charter, told them I was new and coming alone, and drove down to Florida (and came face-to-face with a 350-400 lb. goliath grouper). I hooked up with another non-paired diver as a buddy. Some divers don't like doing this, and I understand why. But, if you want to be an active diver, you might have to, buddies schedules don't always coincide.
A few other things your class might not cover about charters;
-if the water may be choppy...start taking Dramamine (or similar), the night before, and be well hydrated. Believe me, heaving over the rail is not much fun.
-don't board the vessel until the crew OK's it, they'll let you know when they're ready.
-actually LISTEN to the pre-dive briefing...they do this for a reason.
-stow your gear tightly under where you're seated, the crew will appreciate and it will prevent others from tripping or damaging your equipment.
-when exiting the water, approach the ladder from beneath, grab it firmly with one extended (locked-out) arm (very important in choppy water), take off your fins with the other hand, sling them over your arm, THEN ascend the ladder. I can't tell you how many divers I've seen either try to walk up the ladder with fins (bad idea), or take them off before grasping the ladder and then be unable to reach it, especially when there's current.
Anyway, these are the things I realized on my first boat dive. I hope it helps.