The shotgun could be used for birds and for deer with a slug barrel, but that would not be my first choice. The SKS is not much of a hunting rifle in my opinion.
Don't get in a hurry, look around, and learn what is available. You may have enough money to buy an inexpensive (new) shotgun and rifle if you really shop around. You may not have enough to put a scope on the rifle, but you can do that later. More money can buy a truly fine gun, but often only buys a better looking one.
Stick with well know guns in standard calibers .30-06, .270... and you won't be disappointed. The bolt action rifle is the most popular rifle because it is strong, accurate, dependable, and you seldom need/get a second shot.
Over 50 years of shooting, hunting, reading, and studying...