In the 2011 version of the National Electrical Code, there was Table 310.15(B)(7). This table was quite handy for determining the service conductor size. In the 2014 version, it looks like they've done away with this table. However, the long code trail that has replaced it, seems to basically say the same thing.

National Electrical Code 2011

Article 310 - Conductors for General Wiring

II. Installation

Typical services (in the US) are 100, 150, or 200 ampere (though 60 is common for older dwellings). Which means you'll be dealing with a possible range from 4 AWG copper to 2/0 copper (2 AWG al to 4/0 al). Which means you'll want a device that can accommodate conductors from about 0.3 in. diameter to about 0.7 in. diameter, if you want to cover the whole spectrum of possibilities.

I don't think there's a minimum height, but there's a maximum height for breaker handles.

240.24 Location in or on Premises.

(A) Accessibility. Overcurrent devices shall be readily accessible and shall be installed so that the center of the grip of the operating handle of the switch or circuit breaker, when in its highest position, is not more than 2.0 m (6 ft 7 in.) above the floor or working platform...

So for a main breaker panel, where the main breaker is at the top. The center of the main breaker handle, cannot be higher than 6' 7".

Check with the local building department, as they may have a minimum height.

Practically speaking, you'll want it at a comfortable height to work in. You're not going to want to sit, or kneel on the floor while working in the panel.