Apple TV has a built-in update option. A proper functional Apple TV can check for updates without the need for connecting it to a computer. Only when severe software problems make software-resetting impossible, is it needed to restore through a connected computer.
There are many online stores that sell USB cables with all kinds of connectors, including Micro USB on one end. It is not a hard to find item. Just make sure the specification includes data transfer (not a charging-only cable).
The Apple TV (3rd generation) model has its own software version path, and it cannot be updated to the same version as later models. The current version system software for Apple TV (3rd generation) is v7.7.