Hi. What the best method of compression for those files is would depend VERY heavily on what types of files they are, & what was used to create them with - an office program, a video recorder / camera, a database software, an email program, an internet newsgroup server, ... all use different types of data within their files that can be damaged if You perform a bad compression operation on them.
The most reliable method of compressing files is with one of the top 3 software choices - Winzip, WinRAR, or 7zip. There's also a utility used by Macs called StuffIt but that was from a long time ago, I don't think that set of compression routines is used anymore by Macs.
Otherwise, 16Gbs is really not a "large amount of space". Most USB flashdrives for $4US can handle over 32Gbs, & a double-layer DVDR from a $20US pack of 50 blank discs can hold 9Gbs of data, so 2 of those would be plenty to store all the smaller files. And if You got a $70US BluRay-capable burner for Your computer it would hold either 25 or 50Gbs of data per disc for about $1US each blank disc.