Nobody listed ECI.
Cell phone, defensive weapon, and location map of nearest hospitals are always a good idea. Another good idea is to have contact info of your co-shooters family. Stuff happens and it may be non shooting related medical emergency.
I have a tool bag with a rubberized bottom that is my range bag. It stays dry on damp grass.
For competition
The F-Class/Mid Range Prone is all from the 600yd line and the parking is right there. We are shuttled to the targets via pickup. XTC means more walking.
My shooting buddy & I usually just use the same equipment so the mat, scope & rear bag not being moved every time helps.
Rifle, ammo, ECI, Eyes & ears. Add mags if AR.
Clipboard, pens, notebook, calculator & Timer
Hat, water & food, towel, soap, paper towels & at least 1 bag for trash. I keep a few plastic grocery bags as they don't take up much room.
I have a very light shooting mat - it is a ground cover is all but if folds up really nicely.
I don't have jacket, mitt, smoker, squib rod or range cart. Range cart makes sense as an organizational tool at matches.
Pistol matches are less equipment intensive.
For a non-competition trip the gear goes up. Target gear, radios, several firearms etc. I like to keep some items grouped together in a modular format. For example I have a target bag that has everything I need when I go down range to check/swap targets The bag has staple gun & extra staples, tape, pasters, ink pens, staple removal tools. It has a carrying neck strap so I can let it hang in front of me and work from it. Some of the target carriers need to be waded to = rubber boots. At the indoor range I have my own backer I bring. The targets are in a portfolio so the wind won't take them. The fan at the indoor range will do the same. The dividers keep them separated by type. For a match the target bag/portfolio just stay home. I also have specialized gear for certain guns that stay with the gun, IE sight adjustment tools, allen wrench, screwdriver that fits the sights or spare parts.
The particular range may affect the list a little.
I'm always ready to haul off whatever brass I can pick up! That is why I sometimes have kneepads in the list along with a bucket that has 1 flat side on it.