Getting the back up down from 200 GB to 1 GB would be a huge compression that I don't think is going to happen. Ultimately the backup size is going to be at least the size of your database data so take a look at your database files on disk. If it is greater than 1 GB then chances are you aren't going to get it to run no matter what you cut out.
TBH 1 GB isn't much space on any machine, especially a server. I really think you should first consider running the disk cleanup tool in Windows to see if you have lots of temp files to clean up space. After that you probably still won't have room so you need to either consider adding more storage or backing up to something else. This machine seems like it is storage constrained to me.