minimum? i would say just buy the base FFXIV ARR (comes with free 30days sub)
alternative (more days) download the trial version first. (allows you to play up to level 35 and 14 days login max.) then you purchase the ARR (so in a way you get to play 44 days)

to get to the latest content, its going to cost more. have to buy ARR + HW (expansion) not to mention the monthly sub $$ as well.

for the price i am not sure where to get good deals so you will have to search a bit.
can check PSN/STEAM/Impulse/Heavyarms etc. usually they have it

If possible dont get it from steam...Get it from EU SE store. Future sub/mog station item would be cheaper than NA.