Shotgun,
You are asking for quite a lot for under $350, and be able to reach out to 100 yds. You may be able to find a shotgun, with rebates, for under $350. I think Remington has there 870's on rebate now. You will need a good scope separate than what it comes with, if it comes with one. A good scope, recommended/designed to be shot with slugs, will run you around $150+. If you willing to sacrifice and go with a single shot, you will be more in line with what you are looking for. You could also check for used guns as well. I bought a Mossberg 500 combo (slug barrel w/scope and bird barrel) from Dick's Sporting Goods for $379.00, but had to get a better scope. Good Luck.