The classic way to measure gain is to measure only ONE parameter, the collector current. For your purposes it would be easier to measure the collector voltage, you can then easily calculate the current and hence the gain.
The technique is to feed the base from a constant current source, no need to measure it as you already know what it is.
So historically, you would feed the base via a constant current source, and have a milliammeter in the collector, by suitable selection of the constant base current and meter range, you can read the current gain directly off the analogue meter scale.
There are obviously far more complicated methods, but this is simple, easy to do, and should do all you need?.