Do I use 3,3V or 5V, when device supports both?
Using the MAX3232 data sheet , which is what the TTL Converter has on it's board :  

The main difference between using 3.3v or 5v is on the receiver data line "R" (or Rout as it is called on the MAX3232).  

Simply put, you want to power the TTL converter from the same voltage as your Arduino is using (3.3v or 5v). Meaning the voltage that your I/O pins will put out and accept.

The received data line R will go between 0 volts and Vcc.   

You would NOT want to power the TTL converter at 5 volts if you are using the converter for a 3.3v Arduino, as the received data line would go to 5 volts when high. Actually Vcc - 0.1 volts (typ.)  (5 - .1 = 4.9)  as per this specification : 

   

If you power the TTL converter from 3.3 volts, the received data line (Rout) switches between 0v and 3.3v   as shown here :