Recovery mode is a method to force a restore. If you have a backup, you can restore the backup and sync all your iTunes library and contacts - returning everything to the phone. However, if the problem lies in corrupted data or setting that are in the backup, you may have to restore as new, losing some data (not iTunes content)
Recovery mode is where something has gone wrong with the software on your iPhone, so it can't be used. To be safe, you must therefore restore your device.
As longs as all your Music and Apps are on your computer, you will lose nothing. If you restore from backup, your iPhone will be exactly how it was when you last backed up.
Have a great day,