Hi New Diver and great to have you on board.
You can buy the "basic kit" first, mask-fins-slorkel first.
The mask is arguably the single most important piece of kit you will buy, most of us end up with more than one as a result of mistaken purchaces or equipment updates. Use the "place it on your face and inhale via your nose" technique to ensure good seal, ensure easy acess to nose for aiding equalising, also check the hard parts of the frame are not too close to or touching your nose or nasal bridge. Avoid gimicks like valves and tints.
Snorkel is important buy a lower cost unit with a clearing valve on bottom bend, top valve is not as useful.
Green Turtle, your experience is typical and often repeated but it is an instructors nightmare. After over 1000 recreational dives I always use a snorkel, I have needed it twice and on one occation it probably saved my and my buddies life.
Fins, hmmm try as many on at school as you can to compare, all better brand names are OK, again avoid gimicks like splits and look at stiffer options as they allow better control but do require more effort. Dive-Rite offer great fins with steel spring straps as standard, in my opinion best all round value
Booties, sure buy a nice high 3mm ankle pair with zip, colours make kit easy to find on the boat floor.