Well, if you want to go as cheap as possible, but still have a passable weapon, try the following:
Mosin-Nagant M-44 or M-91/30, about $100.00
The M-44 is the better brush gun. Both are powerful, but the poor trigger pull takes some getting used to.
H&R "topper", about $70.00 used; 110.00 new.
Get one in 12ga or 20ga with an open choke (improved cylinder) or a rifled barrel. Use slugs. On Javelina or Deer at 25yards and less, "00" buck is good, if it is leagal.
A Mossberg pump can be had at Wally-World for $200.00-$250.00. Use the same ammo reccomended for the H&R shotgun.
Mossberg ATR, Stevevs M-200, Savage 110, H&R Handi Rifle, Marlin 336, Rem 710. All can be had complete with scope (except 336) for $225.00-$350.00. Get it in .308,.270, .30-06, 30-30(336), any Magnum you can shoot well....Whatever! These are the Cadillacs of low budget rifles.