As for Maintenance, check out this thread: What needs to be checked on a kart and how often - Some thoughts following a discussion with a fellow member
Transport depends on what you have available to you. If you have a pickup truck, you could just put the kart in the bed of the truck and pack your tools and supplies around it or in the cab. If you have a car, you could get a small utility trailer from some place and tow the kart behind you. Harbor Freight: https://www.harborfreight.com/1720-lb-capacity-48-in-x-96-in-super-duty-folding-trailer-62671.html?_br_psugg_q=utility+trailers
As for tools, that depends on your kart. Metric or SAE. Figure out what you have and buy accordingly. Depending on the Level of Wrenching you want to pursue, this could range from a few sockets, wrenches, hex drivers to specialty tools like battery power Drivers, bearing pullers, clutch pullers, laser alignment set, hones, various measuring gauges… you name it, the sky is the limit. You may also want to consider how you plan on storing and transporting your tools and equipment. I have a large two tiered tool box in my garage, but also have a modular rolling tool box I use for my kart tools. https://www.craftsman.com/product/cmst60406/versastack-system-tower Versastack system allows for customizable levels to organize and transport your tools easily with a wheeled base and telescoping handle. Then you can mix and match levels to have what ever you need. Drawers, containers, hardware bins. I love mine.