Hiya, and welcome to BYC!
We've been raising chickens for years and hatching chicks a ton. Our kit is merely a few things: I bolded the two most important you should have on hand.
*
Poultry Cell and Nutri-Drench - vitamins, the latter for weak chicks, the PC for all chicks and chickens.
*Vet Wrap - for splayed legs or curled toes.
*
Hydro-Hen - or similar - probiotics and electrolytes.
*Triple antibiotic ointment (without painkiller).
*Vetericyn antimicrobial spray.
You may sometime down the road need Corid (coccidiosis) or Ivermectin (SLM scaly leg mites), but they have expiration dates, so I'd wait until you may need it.