"I use Time Machine, but it was suggested that storing the information "off-site" would be more secure.
I don't think I'll be paying for Apple's "secure" service again. There's got to be an alternative solution."
Like the saying goes, "fool me once, shame on you. Fool me twice, shame on ME."
I'll offer "an alternative solution" that's cheap and easy:
Get yourself one of these gadgets:
http://www.amazon.com/s/ref=nb_sb_noss?url=search-alias=aps&field-keywords=usb+sata+dock&x=0&y=0
They are CHEAP (some only about $20-25), all work the same, easy to use (did I say "EASY"?).
If you want to spend more, Other World Computing has their "Voyager Quad" docking station with Firewire 400 & 800 and USB3 (I think this one only is bootable via USB, however).
Next, get one or more (at least two suggested) "bare drives" from any vendor of your choice (I like newegg.com as a supplier). They can be either 3.5" or 2.5" drives. You may prefer a 2.5" for "portability" (such as storing a backup off-site, read on).
Then, download the FREE CarbonCopyCloner from:
http://bombich.com/
It's one of the best pieces of software you'll ever use.
When you've got this stuff, attach the dock to the Mac and put a drive into it. Turn it on and initialize it.
Then use CCC to do a "full clone" of your main drive. It will be BOOTABLE and an EXACT COPY of everything on your original. You CAN'T BOOT from Time Machine in a moment of extreme need. The files on the CCC clone will be in POFF (plain ol' finder format). Just mount the drive (in the dock) and navigate to where you need to be, then copy what you wish. No fooling with trying to "restore" from a TM backup.
You can also set up CCC to copy only certain folders (or to exclude certain folders). The developer continually improves his product. CCC can also "archive" old, changed files (stuff that would be deleted when you do an incremental backup to maintain your clone so it's the same as your main drive). This preserves "older versions" of files, as would TM.
If you buy two drives, do TWO backups. Keep one at home (close to the computer). Take the other and store it SOMEWHERE ELSE (different building than the computer is in). If the house (or office) burns down or is burglarized, just get a new computer, hook up your off-site backup, and you're back in business.
A dock and single bare drive will run you less than $80-100. And you'll find that the USB/SATA dock comes in handy for other things, as well.
Hope this helps....