Coming kind of late to this discussion, but I want to commend your for volunteering. Beware! -SAR can be very addictive.

There are a lot of good suggestions here, but I would recommend looking carefully at what older members of the team have found to be useful in your area and on your operations. In your training has anyone reviewed past operations and lessons learned from them?

Mr SAR was in Southern Arizona (about 450 ops, a longtime ago, in a galaxy far, far away so my specifics might not apply to your area. Start with the most reasonable gear assortment you can muster, and tweak, tweak, tweak until you are really comfortable with what you are carrying.

Just a few thoughts:

A good simple cookset is often handy. Trangia was my favorite - dead simple. In colder operations, a team would carry a liquid fuel stove.

Lights are critical, especially a good headlamp. These are much easier to come by nowadays, compared to the 70s. Have more than one, including one on your body

Just be aware that whomever your ICS commander is, Mr. Murphy is really in charge, and he bats last. You made the comment "you are never alone" - Don't count on that. If you do enough SAR, you will be alone at some point, perhaps with a victim to care for. Most searches are over in a matter of hours, but the range can vary from 5 minutes to two weeks (or maybe twenty-nine years - a ranger we looked for very intensively is still missing in the Chiricahuas).

Oddly enough, SAR often comes down to a mental exercise, often quite challenging intellectually, as you try and put yourself in the shoes of the victim.

Volunteer SAR is the most useful, most fulfilling activity I have ever undertaken. I hope you will find it to be the same. Best of luck.