Choice of resistor in half wave rectifier
Is it correct that this resistor is basically functioning as a pulldown for when the AC is in the reverse polarity (top negative)?


Correct. And it is only there to discharge any capacitance in your measuring circuit which might otherwise give a false reading. (The input capacitance on your measuring circuit - an oscilloscope, for example - would tend to hold charge between DC pulses.)


  When connecting the output of this rectifier to the input of another device I think we would lose current across the other device when R1 is too small, so my guess is that we have to choose R1 at least as large as the input impedance of the connected device (or even a lot larger), is this correct? 


If you have a load then R1 is not required. The load will ensure that the voltage falls to zero.


  And if so, is there a more precise way to compute a value?


If you're charging a capacitor in your circuit then look at the discharge time constant.



Figure 1. Capacitor discharge curve. The capacitor discharges by 63% per RC time period. [Image by @Transistor.]

A handy rule of thumb is that the "time constant" of an RC circuit is given by multiplying R and C. τ=RC. After τ the voltage will have decayed by 63%. After 3τ it will have decayed by 95% and 5τ, 99%.