I've been on quite a few juries, and it seems to me that we don't talk enough about how to apply for competitions/residences/whatever.
These tips come from my own experience both applying and judging, so don't take the following post as “the truth” but simply as a possibility. To all my colleagues, please feel free to add your thoughts!
NB: this post is meant to be (hopefully) helpful. I know that calls, competitions, institutions, juries are problematic, but I decided not touch that topic here.
How many scores should you send?
I think not more than 2 (chamber music + ensemble/orchestra). You can send more scores, if you want to, but then you should really rank them, so that the jury knows where to start. (For example, you can name the files in this way: 1-surname_piece-title, 2-surname_piece-title, so that in the folder, they'll appear in the right order.) The jury won't have time to go through the catalogue of every composer, so it is important that you send the most representative pieces.
Recordings
This is a tricky topic. Juries can read scores, so it is not that problematic if you want to send a piece but you don't have the recording yet. Nevertheless, there are some scores that are very difficult to imagine. (I put myself in this category of composers. I worked with experienced conductors and musicians and noticed that many have difficulties imagining the sound of the piece only by looking at the score.) For those scores, having a recording is extremely useful!