Thats fine that just gives me a timeframe to work with. Judging by all the info you provided id say it is a NES or NES clone that you had. most likely a clone as those were more common after 2000

Quick question, what year would you say you had this console? that would narrow down the search tremendously.

But to venture a guess id say NES, that has all the games you listed. Super Mario eliminates anything sega and basically guarantees it was a nintendo of some sort. the SNES also could have been it although the SNES gun controller was rifle shaped with a scope and stock. The gun for NES was pistol shaped. Another thing is that NES was the only system with duck hunt