Arriving at IGI Terminal 3 late at night: best way to handle baggage, SIM and a cab?

Hi everyone, I land at IGI Terminal 3 late at night and could use some local advice. I live in Southern California now and this is my first time back in Delhi in a long while. I tend to over-optimize travel steps and want the easiest, least stressful way out of the airport after a long flight.

My goal is simple: get out of the airport safely and with as little confusion as possible. Can Delhi locals share a practical, step-by-step flow for T3 arrivals at night for someone who will have:

- 1 checked bag

- need a local SIM (or at least data) ASAP

- want to book a cab without getting pulled into random counters

A few specific questions:

1. After immigration and the baggage belt, is there a recommended order for ATM, SIM, and any basic supplies? Or is it better to skip everything and do it the next morning?

2. At that hour, is it easier to use the official taxi booth or just grab an app cab pickup? I am not price hunting, I just want the least hassle and clear signage.

3. Any common mistakes first-timers make at T3 that waste time, like going to the wrong level or exiting from the wrong gate?

For context, my hotel is in South Delhi. Not walking distance, but not super far either. Looking for a calm, efficient plan from people who do this regularly. Thanks!