Glad to see new people interested in hunting, welcome to the board!
For starting out hunting on a tight budget, a good 12 guage pump shotgun with interchangeable chokes would be a good start! You can use it on turkey and with a rifled choke, it will serve as a good deer gun too, at moderate ranges!
An NEF Handi-rifle, with a decent scope, has more than enough accuracy to qualify as a good deer rifle, without breaking the bank! The key with either rifle or shotgun is practice, practice, practice!
Good luck!