Riva:
From personal experience I suggest you avoid DS1307 unless time accuracy is not important. I have one and it looses about 7.5 seconds per day. ...
I also have several DS3231 and they are a lot more accurate at less than drift 2 seconds per month.The DS323x range are more expensive than DS130x but in my mind worth the extra cost.
You get what you pay for. 10 times the price for 10 times the accuracy.
I haven't done it yet, but I am looking at handling the drift in software. Add or subtract a second every few hours.