putting up 3x5 cards at local ranges, gunshops, laundromats, and grocery stores has always worked for me. offer to PAY for the right to hunt, by the way, dont be a cheapskate. that landowner is risking a lawsuit with every person he allows onto his property, so have some respect and rumenerate him for the risk that he is taking! I recommend a used, $400 (probably a scope already on it) Remington 308 autoloader. then you have fast repeat shots to stop a fleeing cripple, for self defense, for dog packs, or running coyotes, and the gas op action lessens the felt recoil, too.
also, 308 milsurp ammo is cheap enough to let you practice a lot, which is needed for a newbie (to powerful rifles). Unless you reload, you are very unlikely to fire more than 100 centerfire rifle rds per year, when you need to fire several thouand rds to build just slowfire hunting ability, and many thousands more rds to build shtf defensive rifle ability. A bolt action is very limiting.
You might want to look into a 243, for varmint hunting year round, and reloading. Remington makes an autorifle in 243, too. the heavy calibers tend to not get used except in big game season, for very, very few shots. The 243 recoils less, and the lighter, 75-90 gr bullets "break up" easily on contact with dirt,, slow down relatively quickly etc, while the heavy 30 cal bullets tend to overpenetrate, richochet, and be dangerous to much greater ranges than 243 varmint type hp's and sp's. For deer, hogs, and pronghorn, tho, the 243 needs the greater penetration of the 100 gr Nosler Partition softpoint.
In order to get the long range, small animal sort of accuracy you want for varmints, you might have to either go with a Browning autorifle, or a bolt action, unfortunately. Or just do as I do and ACCEPT that you are going to miss every other crow or prairie dog at more than 250 yds or so. Big deal. it's just a varmint.
