When I upgraded to a triple,
When I upgraded to a triple, I used:
triple crank: http://www.amazon.com/gp/product/B004V25ZRQ/ref=wms_ohs_product
$44
bottom bracket: http://www.amazon.com/gp/product/B001G0T1JE/ref=wms_ohs_product
$15
You'd also need:
front derailleur: http://www.amazon.com/SRAM-Dual-Pull-Front-Derailleur/dp/B000NNQJ6I
$13
front shifter: http://www.amazon.com/SRAM-X-4-Left-Index-Trigger/dp/B001OQJLJK/
$14
That sums to $84, plus you'd either need to buy or borrow some tools (crank puller and bottom bracket tool) and might need some odds and ends.
So chain ring guard is cheaper. If you have the gearing you need, that's probably fine. I personally like lots of gears.
Regardless, your chain shouldn't be falling off. Can you take a picture of the drivetrain (rear wheel and crankset) with the bike in both the highest and lowest gear? My guess is that your chain is too long and that the derailleur can't handle it. If I'm right (and I may very well be wrong here), the solution is to shorten the chain.
Chain tool: http://www.amazon.com/Sunlite-Series-II-Chain-Tool/dp/B0012GTLVU/
$7
Master link: http://www.amazon.com/KMC-MISSING-LINK-Bicycle-8-Speed/dp/B001AYJF3S/
$9
Where the master link isn't mandatory, but probably a good idea for chain maintenance.
Cheers,
Charles
p.s. In the interest of full discloser, I do in fact own master links. I just, ummm..., haven't gotten around to installing them yet.