Hi and welcome to the forum. Although I don't know diddley-squat about foam board and sign making, I'm sure there's plenty of people here that do. Given that disclaimer, I'd say that if you were cutting the letters/objects free from the foam board, I'd choose a spiral upcut bit that has a long-enough cutting length. In wood, you don't cut deeper per pass than the diameter of the bit, such as 1/2-inch deep maximum cut for a 1/2-inch diameter (cutting edge, not shank) bit. I don't know how the foam board behaves compared to wood, so I'd begin with that rule of thumb to be safe.I am new to sign making and need to choose a router/bits to use on HDU foam board.
My signs will be on the larger side; typically 1" board.
Any suggestions will be greatly appreciated!