I will agree with WTNHUNT. I would shoot with whatever your deer rifle is. I have killed them with my 270, 308, and 300wm. Yeah they are all over kill but they get the job done. With a budget of only $500 you will just be getting alright stuff. I would put that 500 bucks in the sock drawer and continue to save until you reach the 1000 mark. I have been doing a little research trying to find you some good deals and stuff.... I dont know if this guy has this gun anymore or who he even is, but you could find out through the website he posted, this is a pretty good deal on a nice gun and decent scope.
http://longrangehunting.com/forums/f25/sale-ruger-target-model-m77-22-250-a-38188/
this is pretty much what I shoot, i have a little different set up but close enough in price for the rifle and scope combo. i have a ruger rifle and leupold scope......
http://www.gunsamerica.com/939778931/Guns/Rifles/Ruger-Rifles/1-Type/Ruger_22_250.htm#
you can expect to pay just under 600 for a ruger. Anyhow, what is your gun of choice and scope of choice if you could get what you wanted? I will do a little research and see what kind of deals I can find for you.