I'm working on my initial equipment. I'm buying a level 1 computer (miniaturized with Range I). Can I use it for hacking, and/or do I need to purchase a hacking kit?
You need it for remote hacking
You only will require a hacking kit if you are remotely hacking a computer. Otherwise, if you have physical access to that computer, you don't need a hacking kit at all.
From the Computers skill description (p. 137):
If you don't have physical access to a computer system's user interface, you must use a hacking kit to access and manipulate the system.
The description of User Interfaces can be found under Computers (p.213), on the Equipment chapter, which, once again, will state:
You can use a hacking kit to access a computer without using a user interface, but this requires you to have physical contact with the computer or to make contact through an infosphere or similar network that is linked to the computers.