Software: Wire should be fine. Of course, you usually will want libraries for each device. This particular ADC is designed for automotive use and I could not find a specific library for it so you are correct that you will need to speak with it directly. Here is the DATASHEET
I2C Hardware: On the Arduino Uno, SDA is A4 and SCL is A5.
One thing you almost always have to do with I2C is to provide a 10K pull-up to +5 on each pin (SDA and SCL) - I use a small breadboard whenever I use I2C, so I have power, ground, A4 and A5 available for pullups and multiple devices.
The reason for this is that the I2C bus is active-low. It signals by pulling the pins low in sequence to communicate.
If you already had the DS3231 RTC module on the same bus, which apparently you do not or you would not be asking this question, then you do not need your own pull-ups because the RTC includes them internally.
It might be easier for you to use a different I2C ADC such as the ADS1115.
Here is a generic search that shows the module:
Here is a generic search which shows the software side: