B&B,
$150 bucks is plenty of money to get you on the water in a decent, 8'-9' pram. The catch, of course, is you're going to have to build it yourself, and getting marine-grade plywood might be difficult. But there a dozens of free plans available, and building a boat that rows decently and is stable enough to stand and cast from doesn't require more tools than most home-owners already have. Also, you're going to have to build oars, because what is sold is heavy, unbalanced junk.
If this is a first-time build, figure on at least 100 hours of work, from start to finish, and 150 hours is more realistic. If 1/4" ply is used and you don't go crazy with the framing, figure on a finished weight of about 5.5 pounds per foot, or a boat you can pick up and carry.
Here's one more hassle, though manageable. You'll need a way to transport the boat and a way to store it, so that sun and weather don't trash it. Therefore, when all is said and done, trying to find a cheap, used kayak might be your best path, as others have said. But if you want something that offers a bit more leg room and the chance to stand to cast, a simple, flat-bottomed, single-chine pram is the way to go. And, no, you can't be hanging an outboard or electric motor on such a boat. Those need a different and beefier design.
And, yeah, I've built a lot of them for my own use, and well as given a pair of such prams to a kids summer camp. So I know my cost estimates are realistic.
Charlie