Everybody here seems to use the palomar knot. I use the san diego jam knot, never had a problem with it, although I have not used it with braid before. http://www.animatedknots.com/ is a good place to check out.
A trolling motor is a big convenience. There are lots of times I wish I had one (ok, like ALL the time), but I just fish with an anchor. Generally I try to figure out which way the wind is going to make the boat drift and start as far upwind as I can, then just lift the anchor to move the boat. As for batteries, I would suggest getting a 12V trolling motor if you get one, and then yes another battery for the motor and possibly tie the fish finder into the second battery as well. Getting stranded on the lake with a dead battery is never fun. Over the winter, keeping your battery on a standard battery charger isn't the best idea. Like kingkong said, you want a trickle charger and generally I just put it on to keep it fully charged every couple weeks in the off season.
As for the kayak, I've never had a FISHING kayak, but generally it seems a LOT nicer fishing from my 16' Old Town (circa 1920) than from a kayak. If your canoe is the square stern model you can always slap a stern mount trolling motor on it.
Good luck and happy fishing!