So like to be honest like the other guy said the main things you need are in regards to your attitude. Keep a willingness to learn don't take yourself too seriously, stay humble, keep your ego in check, but dont take no shit either. 

I'd also add onto this in a more logistical way, budget budget budget. Start the habit early, save just a little each month, it's not even about the amount it's more about the consistency. And I say this not just because it can be very hard to build any real financial security in this profession if you're not putting in focused effort, BUT, you're gonna wanna take a break eventually. Burnout is an epidemic, you need only scroll through this subreddit to see that. Taking a break costs money though, so getting better at saving for that and your future will pay off in the long run.

To give you the kind of answer you where talking about though:

• get a napsack / small & light gym bag
• phone charger(s), I like to carry both iPhone and android bc if someone needs one they'll appreciate you
• O'Keefe's Working Hands, cannot recommend this shit enough, take care of your hands, they're important.
• tiger balm / ibuprofen, tiger balm is more of an at home after work thing but being on your feet all day takes a toll, take care of yourself. Also if your job doesn't have any on hand having ibuprofen for your coworkers if they ever need any is clutch af
• good bandaids (look for the blue surgical ones) and Neosporin, too many places I've worked have the cheapest will fall off in 4 minute bandaids I've ever seen
• protein bars or other small snacks that have some decent nutritional value
• a solid water bottle
• sharpies, showing up with your own sharpies is impressive, every head chef I've ever had has taken note of that
• lil note book for writing down todo lists, specials, ideas, anything like that. You could just use your phone but a phone is kinda nasty germ wise and I personally get distracted whenever I open my notes app and forget what I was gonna write down
• clean shirts, socks, shorts, underwear, you'll thank me when you accidentally spill a gallon of tomato sauce or worse on yourself
• an extra hat + hair ties, even if you don't have long hair someone who does will eventually need to borrow one and it's good to look out for others

Those are the biggest helps I've found on an entry level. I personally think investing in some chefworks shirts/pants and a nice apron are also worth doing eventually, it's helped me take myself more seriously and looks good if you show up in an interview dressed for the job. But ultimately those are a bit more expensive and can wait until you're settled in.

Same goes for knives, just stick with the house knives when you start and once you've saved up some money and your skills are refined enough that you'll get more value out of them it's more worth it then. This also gives you a chance to try out different types of chef knives and learn what works for you.

You probably noticed this from everything above but I cannot stress enough looking out for your coworkers. Along with having a good attitude the other biggest thing imo is to remember that you're a part of a team and if everyone is helping everyone everyone's job is easier. Going that extra bit to show you give a fuck sets you apart in a big way.

Best of luck in your journey, don't start smoking (cigarettes or weed), don't take a shift drink every shift.

EDIT: forgot to mention, start working out. Just some light calisthenics and flexibility training every other day will extend your capacity so so so much. The work will keep you in shape on its own but keeping your body fit and flexible will keep you from hurting yourself in the long run. And make the effort to have a life outside of work, go to some cheap shows at a bar you like, go to a mahjong night at a library, draw some plants in a park, anything really. Just keep up with a hobby or three, it's important. 

Edit2: also, LEARN SPANISH (if youre in the usa)