The chefs coat is fine, if they aren't providing it it's likely not a super professional place. Every restaurant I worked was very strict on uniforms and as such they provided everything.

Don't bring knives. If you really want to eventually start bringing your own knives get [Mercer Millennia like these](Mercer Culinary M21820 Millennia 8-Piece Knife Roll Set, Black https://www.amazon.com/dp/B005P0OLA0/). Although I would probably recommend buying the individual pieces so you don't get anything that you don't want and only get what you do. Don't get expensive knives, they aren't worth it for a position like yours unless it's something you really want for personal enjoyment. Just be careful with knives being stolen which is one of the reasons why you don't want anything expensive. A big advantage of cheaper knives is if they do get stolen it's easy to demand the employer replace them. They'll fight you on expensive knives.

You are absolutely going to be overwhelmed. That's normal for everyone. I am just about the most well trained chef there is. BS Food studies from NYU, MBA with a focus on restaurant management from CBS, two year long apprenticeships at separate three Michelin star restaurants, etc. I was still nervous, intimidated, and overwhelmed when I started my job. Being nervous is nothing to well... be nervous about.

Good luck.