One does not usually compress a drive in order to gain speed. Sure it creates space on the disk, but any data read has to be decompressed again before it can be used. It is questionable whether the faster read compensates for the additional time taken to perforn that decompression. If you beleive lack of disk space is the reason for the lack of speed, then delete or back off stuff you don't use, as you have considered, or buy/install a larger drive.
Without knowing the drive and being there to see I think it an impossible task to say exactly what can go, but try something like CCleaner to clear out comon culprits. Be aware it's default settings does mean you can lose things like history and cookies though.
You are sure the drive space really is the issue ?