Don't despair, just take your wheel down to the shop and ask them what they think.
Repairable? If so, it might end up being about $15 labor. Spokes are very inexpensive, something like 20¢ each.
It may be the case that the hub bearing is disintegrating too. If your wheel is attached to the bike and you can klunk it side-to-side at the tire, the bearings are loose or disintegrating.
At any rate, if the bearings are failing or if the wheel's too bad to fix, a new rear wheel with acceptable-quality bearings is going to range from perhaps $20 (for a steel-rim/steel-hub freewheel style) to perhaps $60 (for an aluminum-rim/aluminum-hub style equipped with a built-in ratchet unit for the gears, aka a "freehub"). I'm gauging those prices based on your description of the bike as being not a "bike-shop" brand; obviously there are high-end wheels that go beyond this price range.
The shop will probably charge $5 to $10 labor to swap your parts over, and might be able to do it on the spot since it takes just a few minutes. Try to hit them at an off-time, like in the morning on a weekday
edit: I want to add that if your frame is pretty thin where the wheel's axle rests, you should stick with bolt-on axles even if you could get a quick-release one, because quick-release mechanisms have trouble on thin "dropouts" (as we call the place where the axle slides into the frame). If you're not sure what to consider "thin," take the whole bike in and bring up the issue.