Thin wetsuit is the way to go, with maybe a fleece over it.
If you do fall in, without one, you could lose too much body heat to make the shore, plus even a 3mm will give a lot of bouyancy, and it isn't too hot when you paddle.
I was really lucky last year, we have a german supermarket chain, they have small stores, but have different offers every week to make up for the small range, and their prices are really low. One week they offered 3mm full wetsuits for $60, good quality too, then the next week it was fishing gear, and I got a tiny waterproof fish finder for $60, pretty basic, shows depth and fish, but not bottom structure, but for that price who cares, its good enough.
Maybe try getting one on the net, probably expensive for you locally