This is very subjective. I suggest thinking about a pilot-study size that works budget-wise, and from that figure out the df you'd have for error, and also see how badly or poorly that works in terms of underestimating N and decide if that's tolerable.
If it is not tolerable, you need to try a larger pilot size and corresponding larger df. Or perhaps it's overkill and you reduce both.
The consequences of underestimating N are really critical if it would mean waiting a long time or encountering hassles to get more data, e.g., having to wait a year for the next planting in an agricultural experiment. In a situation
where you could easily and quickly get more data, it's considerably less of an issue if your estimated sample size is too small, because you can just run another quick follow up experiment to bring it your estimates to the precision you require.
A simple example: you decide to just test two of your treatments in the pilot to get an idea of the error variance. If you try 5 obs per treatment, the pooled SD would have 2*(5-1) = 8 df. Run that through the app and see how that
looks. If not good enough, maybe you want to bump it up to, say, 8 per treatment (14 df); etc.