Looking back, I’d say the following were essential for me.
Bag: just something to keep your crap in. Doesn’t have to be an expensive flight bag, I used an old backpack until well through my training.
Headset: I got the Asa HS-1, gel ear pads and ear pad liners. $120 and they were comfortable enough. Don’t wait for your “forever” headset: they’re never forever anyways, you’ll need a set for your passengers, and it’s not worth the frustration of every set in the trainer being broken somehow. You’ll save a lot of headache by getting them now.
The usual paper stuff: E6B, plotter, standard calculator, some charts, a pencil. Your linstructor will give you more info about this.
Foggles will be needed for at least 3 hours.
Neutral colored, non-polarized sunglasses
Flashlight, a good one with red and white LEDs
Fuel tester. Doesn’t have to be a good one, but you’re going to be really bummed when you get out for a solo flight and the one in the trainer is missing.
Gloves for preflight. You WILL bust your knuckles trying to get a dipstick out in the winter, and you will yell expletives. Learn from my mistakes.
I’m a big iPad user, so that tops the list for me. I used ForeFlight on an Air 2. But if you’re buying, go with the pro and the pencil, much easier to handwrite notes with. I kept everything I used on my iPad but I guess it depends on the instructor. Mine didn’t really care as long as I could do it the paper way too.
If you don’t have GPS built in, you’ll need something to do that. I built a Stratux box but there are many good GPS-only units out there.
Kneeboard: I’ve used the Flight Outfitters and the Flight Gear HP ones and I like the Flight Gear better for all but the longest of my flights. Plus it’s cheaper and actually protects your iPad when it’s closed.
That’s what I got through training with for the most part, with some additions/modifications for 20/20 hindsight.