first off, I would go with something in the most common cals; 762.39 243 270 30.06 308 3030 7 mag, and let us throw in 6.5 swede. All these cals are easy to find, can be had anywhere at stores, gunshows , etc., also they can be had relatively cheap.
Now if you want to be able to take down anything in N. america, then a 30.06 with 200 plus grain bullets will do the job, if you want to keep it dear size or smaller, then the 243 will fill the bill. the 270 and the 308 will do everything else.
Lastly , you should be able to go to any of the big box stores, and get a rifle with scope package for 500 bucks or less. such as howa, savage, remmy, winny, mossberg, etc. You may realize, that as a huge cz fan, I have 4 , the cz is beautiful, light, and super accurate.