I had a savage 110 in 30-06. I would reccomend that rifle. Trigger and bolt action weren't the smoothest, but great accuracy for the money. I kept the rifle in the back of a farm truck a lot. Never a problem with it, and I abused it.
Stay away from remmington 770's, remmington 700's and ruger 77's are good and I have used both of those in varmit cartridges. coworker has a very accurate tikka t3 stainless lite model in .270. I know shooting sports are very popular in texas. While you shop for a gun purchase ammo. $20 a box is a good price over in NY. Consider 1 or 2 boxes a year until your old n grey as a supply. Restock as needed.
Look at the places you plan to hunt. Pick 5 spots where you see some good tracks and signs. Now pick 2 spots in each of those areas as a good place to hunt from. If you're seeing places with 300+ yard shots, go with the .270. If you're seeing less than 300 yard shots, go with the 30-06. If it's all wooded and your rarely seeing a clean shot past 150 yards, a .30-30 will do. Also, .243 is a very nice caliber. Will be good for 200-300 yard shots with great accuracy. Wouldn't use it for anything bigger than deer though. Also, this rifle has light recoil and would work well If you have a wife and kids who'd like to shoot too.
I hunt in the woods and only on deer and black bear. 30-30 is the caliber I use. I am in the market for a .243 though. Keep the rifle open sights until you can afford some quality glass for the rifle. nikon buckmaster, Burris full field II, and nikon prostaff have all been reliable for me. All of these run about 150-200. Purchase good rings for them too. Preferably with 4 clamping bolts per ring. Weaver mounts and rings have been a poor choice in my history. At some point before hunting season, remove the scope and make sure the iron sights are lined up, if the rifle is equiped with them.