I deleted a couple of other comments because they were snarky. The combination of "must have" in the title, and a website dedicated to advertising, triggered something.
But it's fine to participate. Welcome to the commuting forum!
I've had so many discussions with people who express an interest in cycling to work. People are nervous about it until they experience it a few times, then it's OK. So I try to reassure them by avoiding lengthy lists of necessities and precautions. Most of them have a serviceable bike. Practically all newer bikes such as hybrids from decent brands come with puncture resistant tires. At my workplace, they will find a way to bring their bike indoors, as I do, or lock it in the rack which is reasonably secure. Everybody knows about helmets these days, and they don't need to be told. The reason is that we all make our kids wear helmets. Most will hang up their bikes in the fall before it becomes necessary to think about lighting. Most will continue to drive their cars if rain is likely or when they need to haul something heavy or go on an errand during work hours.
Let experience be a guide. There's nothing wrong with trying out new accessories, but you have to decide when they become burdensome or if there are better alternatives such as keeping some necessities at work.
A bigger issue for most beginning commuters is contending with urban riding and finding a route that they're comfortable with.
So it really works to just get on your bike and ride, and figure out what accessories you need by trial and error. I've actually stripped down my bike since I started commuting regularly. Today I'm down to a single speed that I threw together from spare parts, and a lunch bag that I can hang over my handlebar.
I realized (thanks to comments in this forum) that I'm never more than 2 miles from either home or work, which I can walk in a jiffy. So I don't really need to worry about repairs while on the way.
Thanks to free software and the cloud, I don't need to carry any kind of computer related stuff.