With shotguns (as with most other things in life) you generally get what you pay for. Would you risk your safety, or that of your family, on a "cheap" shotgun? I wouldn't, and I'll bet you wouldn't either.
My best recommendation is to stick with the time-proven name brands like Remington (e.g., their venerable Model 870 pump-gun) or Winchester. Take some time to visit your local gunshop and compare these with the "cheap" brands: the differences will be largely obvious. Ask questions about the reliability of each model, do your homework, and I'm certain that you will find a shotgun that you can both afford and rely upon.
Good luck, and good shooting!