Cheapest? You could grab a butane lighter but for a few bucks more you could get a pencil torch. They're pretty cool and small enough to put in your pocket... I'm not sure if you have a Harbor Freight Tools near you but that's where I got mine.
I just squirt some Star San on it with a spray bottle. I would be leery of using a torch to sanitize it. Wouldn't take much to overheat a spot and cause some cracking or chipping. Plus, since I keep a spray bottle of sanitizer around the brewery at all times, it is easier than flaming.
I just use starsan. You can use an alcohol lamp like they use for yeast. You don't want a super hot flame . I had a friend who used a propane torch (like for sweating copper). it worked well for a while but one day he just ended up cracking the neck of the carboy with the heat.
EGADS! 3 MONTHS WITHOUT BREWING? MOVING YOU SUCK.... NEVER AGAIN
In Kegerator - Hopfen Weiss, Best Bitter In Primary - Baby Baine Barleywine Next up: Petite Saison