How do I determine which radial intercept angle to use?
There is no definite answer to this question. 

If you are far away from the beacon radials are far away from each other and thus small intercept angle would be insufficient to reach desired track in feasible time. Also, if you are, say, five miles away from the beacon intercept angle of thirty degrees would be acceptable for C172 but an overkill for transport category jet traveling at 450kts of ground speed. Then again, the mentioned jet would assume the same 30 degree intercept angle to join final track for an approach. 

The question has also to do with current aircraft track in relation to the desired track. If you are for example tracking radial 150 inbound towards a beacon and you want to change to radial 180 an intercept angle of 30 degrees would keep you on radial 150 and you will not intercept the desired track until you are overhead the beacon.

The only rule seems to be that when vectoring for approach ATC gives a maximum intercept angle of 30 degrees.