Should I attach a current limiter to my jerry-rigged power supply?
does AC amperage and DC amperage mean different values like how it
  does with voltage?


Yes. A transformer rated for 1A AC may not be able to deliver 1A DC through a rectifier and filter capacitor. The main reason for this is that the current is drawn in pulses as it charges up the capacitor, so the heating effect in the transformer windings will be higher than for a purely resistive load. In technical terms the 'crest factor' is higher, so the rms current (and loss in the winding resistance) is greater.  

On the other hand, the DC/DC converter will draw less current from the supply when set for lower output voltage, since it 'transforms' the power from high voltage at low current to lower voltage at higher current. 

If the filter capacitor is not big enough to hold the rectified voltage above the minimum that the converter needs to operate then its output voltage will drop and limit current. A much larger capacitor will hold the voltage up better between peaks so the converter will draw less current for the same output current, but the pulses will be shorter so the rms transformer current may be higher.      

So how much current you can get out of the converter without overheating the transformer depends on its output voltage and (to a lesser extent) the value of your filter capacitor. 

Here is an example simulation of a 16VAC transformer with bridge rectifier and 1000uF filter capacitor feeding a high quality DC/DC converter which is delivering 12V at 1A to a 12&ohm; resistive load. (blue = filter capacitor voltage, red = transformer current, green = DC/DC output voltage). The peak transformer secondary current is 3A, and the rms current is 1.3A. In comparison, if a 12VAC transformer was powering that same load directly the (AC) current would be 1.4A peak and 1A rms.