Chances are that your Android device is attaching itself to your computer as an MTP device. Most file managers and music players should recognize this, but there's a chance that they're not.
I would use Clementine, it does everything that you want it to do.
Note: If Clementine does not recognize your device, make sure
gvfs-backends are installed (
sudo apt-get install libmtp-common gvfs-backends from a terminal)
In order to sync only part of your library, you would simply create a new playlist and add everything you want to sync to your device. From there, you would select the whole playlist (Ctrl+A) and, in the right-click menu, choose "Copy to Device...", and tweak the settings to your liking.
Clementine will automatically transcode music when you sync it. In order to do that, go to the Devices tab, right-click on your device and select "Device Properties...". Under the "File formats" tab, select "Convert all music" and select the format you want to be on the device.