Maybe you should rethink a .308 Semi-Auto Carbine for under $1,000.00.
In that price range you would perhaps be better off looking for something in 7.62x39 or saving up until you have a little more cash to drop.
PTR-91 will run you about $1,000.00 but they are by no means light. AK's are not that light either but the ammunition will be much less expensive.
Of the creatures you listed below the only one I am unsure of would be 7.62x39 vs a Bear. I have not and do not know anyone who has had to shoot at bear with an AK or SKS type rifle. Despite what you read; you can hit man sized targets out past 100 yards with an AK style rifle.