welcome,
as eager as you are to get out and hunt
first, slow down,
just getting your hunter ed, and new to hunting
i would not recommend going out hunting big game just yet,
first step is getting out in the field,
learning the land/animals,
also when you get your shotgun, practice first before heading out in the field with it,
any ranges nearby? public or private? have your own land to practice on?
hunter orange requirements will vary by state, will be covered in your hunter ed course
whether its required or not, i highly recommend it.
in NY hunter orange is optional, and i wear it even when on my own land,
other states have various regulations, certain amount of sq inches on head and body,

remember hunter ed will teach you the basics to hunt safely and ethically,
they will not teach you how to be a good hunter, that will take time,

for safety your gear will vary, how far into the field you plan on going, how long you plan on staying out,
basics safety gear, first aid, compass, fire starting kit,
hunting alone, let someone know your plans/route/how long you plan on staying out,
heater? not at all,
if your not comfortable being out in the cold, keep your day short, and learn to properly layer your clothes,
field dressing a dear isnt difficult, doing quickly, efficiently, etc will take time, basic field dressing will be covered in hunters ed,
as for butchering the deer recommend taking it to a deer processor nearby, find 1 or 2 ahead of time so your not scrambling looking after the fact.
wouldnt be concerned about the weight
smaller deer = less meat, but generally easier to harvest a smaller deer,

while your waiting on your license, there is nothing stopping you from getting out in the field, scouting, finding spots,
get your gun and practice,
also have you thought of small game?
deer seasons are usually pretty short, but small games are usually available most of winter