May I also suggest the Ruger American rifle. It comes in calibers of 243, 270, 308, and 30/06. Take your pick. American made and is priced very well under $500.
http://www.ruger.com/products/americanRifle/models.html
Welcome to the rifle world and good luck on your journey. Just to relate to you, I was an avid pistol-only shooter before and made the transition to rifles on my own without any assistance. You'll be fine if you do your research, practice, and be careful with handling firearms as always.
I can definitely understand that Budget sometimes dictates your choices. In my case I started with an all-purpose AR15 rifle in 5.56/.223, then another AR in 300BLK, then finally a bolt action Mosin Nagant. The process may take months to acquire the funds you need, so be patient.