I would check with the Dive Op about buddies. While insta-buddies are always an option (where 2 single divers are paired as buddies) most dive ops who already put a divemaster in the water will let you buddy with the divemaster, usually at no extra charge (but confirm that). If you specifically ask for a private DM, there is usually a charge. Note that in some places (Florida panhandle, Myrtle Beach, etc.) it is common for them NOT to put a DM in the water -- so you'd either need an insta-buddy or they might make you pay for a private DM.
As far as Dive Ops, I usually check on here, TripAdvisor, and their Facebook page for reviews. On sites like TripAdvisor where it's easy to search, I'll look at the lower reviews especially (if they have any) to see how old they are and whether they sound like safety issues or just sometimes people/businesses don't click. I do think the suggestion of Rainbow Reef above could be a good match for your first trip.
As for luggage, my son and I each have the largest size bag you can check on flights (I believe 31") that we mainly put our dive gear in. My bag is a hard Samsonite F'lite (basically a plastic shell with 1 divider) and his is a regular nylon bag, and I have to say his is showing signs of wear -- though we try to dry things before we travel, sometimes things are still damp, especially when we take 5mm wetsuits (this adds weight too). As someone mentioned, we avoid using bags that have scuba branding on the outside -- both because of possible theft, and because some airlines/ferries might want to charge extra. We use these big bags for scuba gear, and we carry on 24" duffels for our clothes.
P.S.: Watch the fine print of some of the discount airlines as far as maximum weight for checked bags. We are always above 40 lbs. on our scuba bags, and a few discount airlines (I believe Spirit is one) have a 40 lb. limit and then charge a big fee for going over that weight.
