It's your first beer so you want to get in there early.
After 4 days put one in the fridge in the morning and try it at night. It will be lightly carbonated but probably drinkable, and you will know what your beer tastes like.
After that it will get better. The trick is to leave them out of the fridge unless you plan to drink them, since they won't carbonate while in the fridge.
3-4 weeks with 4 being "better" IMHO. You will have carbonation in the bottle faster than than but it takes a bit more time for it to be "right". You should notice a change each additional week until about 4 weeks.
If you have enough bottles please try for yourself by sampling each week.
I've had carbonation after 4-5 days. Depends on the style for how long to leave it. I usually start drinking IPAs after 5-7 days. Other styles can take 3+ weeks in the bottle to hit their prime. A nice big stout could take many months.