Well, I dont know what kind of system you are controlling (perhaps you should mention it), but a sampling period of minutes seems very long. I could *maybe* understand seconds for a hot-plate or something. For motor control and positioning, I was thinking along the lines of milliseconds or even useconds.
The value of ki will depend much on your system, but some of mine have ki around 0.1, 0.2, 0.4, etc.