Which is better for navigating shallow, narrow streams: a canoe or a kayak?

I don’t have any experience with either canoeing or kayaking, but there are some (calm) streams and rivers in my area that I’d like to explore. So I’m wondering which would be better for maneuvering in narrow and shallow water. A canoe or a kayak?

(I know someone is going to recommend that I rent each before I purchasing one or the other, but by the time I rent a canoe for an hour and then a kayak for an hour, that’s already 25% of the cost for just buying one used from Craigslist. I’m very excited about this and I’m sure it’s better for me to buy used first instead of renting something first. I’ll probably end up buying both a canoe and a kayak eventually, but I’d rather get the one that’s better for shallow water first. )