Is there a way I can choose what individual files to download within a .torrent?

In µTorrent as well as clearing the "Don't start the download automatically" option, enable the "Show a window that displays the files inside the torrent" option.

This will give you dialog in which you can select which files you want to download before it adds the torrent to the download list.

Download with magnet link, then stop pause it, and you can see list of files at bottom, right-click on the file you don't want to download, and click on Don't Download

Yeah, there is a setting under uTorrent that reads "automatically start torrents." Turn it off. This will torrents load into it in a stopped state. Also make sure uTorrent isn't loading torrents from a directory. It can scan a directory and will load torrents automatically. Make sure not to put your torrent there.

This is something really dependent on the torrent software you are using. For example on Mac, as I remember from my last exprience µTorrent doesn't provide such option but Transmission does. I think Azureus(Vuze) is the other option you can consider it.