Lights are life support, and I'd try to avoid buying junk.
On the canister vs handheld, there are some decent handhelds out there these days so it'll really come down to personal preference. One advantage of a canister is that the battery weight is on your hip rather than your hand, but one advantage of the handheld is that it's a smaller more compact package without the cord (a potential failure point).
Watch out for advertising that talks about Lux and advertising that talks about Lumens. They're different beasts with wildly different numbers (700 lumens, 10,000 lux). Making sense of those things and the various manufacturer numbers would require a PhD in optical physics, or at least it feels that way sometimes, but the simple answer is "lumens" is the total amount of light output, and "lux" is a number that gives the light output at a fixed location a set distance away. So make sure when you're comparing "lux" numbers you also are comparing the distance from the head.
More information on Lumens vs Lux can be found at this link:
Evaluating LED Technology - Halcyon Dive Systems
The things I find more meaningful and useful once you get beyond ~700 lumens are the kelvin ("temperature") of the light and the beam angle. Note, a tighter beam will increase the lux numbers at greater distances.
Kelvin wise, the higher the number, the whiter the light. Once you start going above 6000 kelvin you'll see the deep blues in the water and the colors of the formations will really "pop".
Beam wise, look for something with a tight focus for signaling. A "bright light" that does not have a decent spot, while pretty, is also pretty useless when trying to signal someone. 5-6° with spill is a good starting point, less spill is better.
Primary lights should be rechargeable. You're going to use them every time you go cave diving, there's no need to fill up the landfills or recycling centers with disposable batteries.
The competing battery technologies have pro's and cons. While most Lithium Ion and NiMH batteries are OK, you'll want to avoid LiPO. If you find a used light using Lead Acid (yes, they're still out there) be aware that they're going to be heavy as hell, but it's cheap to replace those batteries.
Burn-time wise, 3 hours is a minimum. While you may not be doing dives of that duration anytime in the immediate future, you will likely be doing multiple dives a day and the total time may add up to ~2 hours. An extra 50% burn time is never a bad thing.
If you're buying used, there's a wide selection of really good lights that as AJ said, could be found on ebay or forums.
I personally prefer lights made by Light Monkey, Dive Rite, and Halcyon. My bias is because they're all within a 30 minute drive from my house and have great customer service; if I have a problem I can drop the light off at the company, go grab lunch, and pick it up after lunch.
My current go to is a 21W HID, which is old technology but packs a decent punch. I think the 12w-5.2amp LED lights are pretty decent starting points and will serve someone just getting into this well. I'd love it if someone were to give me a Halcyon Focus, that's a pretty light and in clear water is excellent.
Bobby's lights (uwlight dude) seem OK, but I've only used one once and he's in another state so I don't have the quick lunch turnaround with him and that's the only reason he's not on my list.
As I said in the first sentence, in cave diving lights are life support. Avoid the cheap crap.