The amount of bass can be controlled with a turn of the knob to get the desired level you want. You will be amazed at what subtle sounds you can miss by having a sub par sub. A better sub will make a huge difference, and you don't have to crank it up loud to notice the difference. I have a Yamaha powered sub on my computer and its 6" and a mere 25watts, but man does it put out some bass. It puts the 8" passive Pioneer sub that's in my bedroom to shame. The sheer weight of the thing is pretty amazing for such a small sub, but that's what you get from quality construction. I think the Yamaha and the Velodyne subs that I suggested will give you the tighter bass of the bunch.
THIS place out of New York ships to Canada and they have the Yamaha for $89.99 so you can probably get the total price somewhere around your budget when you account for shipping. I've ordered from J&R before and their service is excellent.